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Describes how distinct surgery presentations of a given 3-manifold are related
In mathematics, the Kirby calculus in geometric topology, named after Robion Kirby, is a method for modifying framed links in the 3-sphere using a finite
Kirby_calculus
American mathematician
topological manifold. He also proved the fundamental result on the Kirby calculus, a method for describing 3-manifolds and smooth 4-manifolds by surgery
Robion_Kirby
Topics referred to by the same term
also known as Kirby, the only dog to have won all three major international dog shows in the same year Kirby calculus Kirby Krackle (or Kirby Dots), an artistic
Kirby
Operation used to modify three-dimensional topological spaces
presentations of a given 3-manifold might be related. The answer is called the Kirby calculus. Hyperbolic Dehn surgery Tubular neighborhood Surgery on manifolds,
Dehn_surgery
Mathematical space
I. (1999), 4-Manifolds and Kirby Calculus, Grad. Studies in Math., vol. 20, American Mathematical Society, MR 1707327 Kirby, R. C.; Taylor, L. R. (1998)
4-manifold
One of three types of isotopy-preserving local changes to a knot diagram
change the crossing number of the diagram. In applications such as the Kirby calculus, in which the desired equivalence class of knot diagrams is not a knot
Reidemeister_move
Manifold union
smooth manifolds. Casson handle Cobordism theory CW complex Handlebody Kirby calculus Manifold decomposition S. Smale, "On the structure of manifolds" Amer
Handle_decomposition
Smooth 4-manifold homeomorphic yet not diffeomorphic to Euclidean space
4-manifolds and Kirby calculus. Graduate Studies in Mathematics. Vol. 20. Providence, RI: American Mathematical Society. ISBN 0-8218-0994-6. Kirby, Robion C
Exotic_R4
Type of surface topology
which one can perform surgery. In fact, clasper calculus can be thought of as a variant of Kirby calculus on which only certain specific types of framed
Clasper_(mathematics)
Topics referred to by the same term
Slam-dunk (mathematics), in low-dimensional topology, a useful move of the Kirby calculus Smash (tennis), or slam dunk Sister's Slam Dunk, a South Korean variety
Slam_dunk_(disambiguation)
on a framed link. Robert Gompf and Andras Stipsicz, 4-Manifolds and Kirby Calculus, (1999) (Volume 20 in Graduate Studies in Mathematics), American Mathematical
Slam-dunk_(mathematics)
Concept in differential geometry
ISBN 978-0-8218-2055-1. Gompf, Robert E.; Stipsicz, Andras I. (1999). 4-Manifolds and Kirby Calculus. American Mathematical Society. pp. 55–58, 186–187. ISBN 0-8218-0994-6
Spin_structure
group Writhe Quandle Seifert surface Braids Braid theory Braid group Kirby calculus Genus (mathematics) Examples Positive Euler characteristic 2-disk Sphere
List of geometric topology topics
List_of_geometric_topology_topics
UK Parliament constituency (since 2010)
constituency is 50.4% Christian, 41.9% no religion, and 7.7% other. Electoral Calculus categorises the seat as being part of the "Strong Right" demographic, those
Clacton_(constituency)
Indian mathematician and scholar
Mumbai in 2006 for a thesis titled "Knots, mapping class groups and Kirby calculus", and MSc degree from Maharaja Sayajirao University of Baroda, Vadodara
Dishant_Mayurbhai_Pancholi
4-manifold invariants
Press Gompf, Robert E.; Stipcisz, András I. (1999). 4-Manifolds and Kirby Calculus. doi:10.1090/gsm/020. ISBN 978-1-4704-7455-3. Nicolaescu, Liviu I. (2000)
Seiberg–Witten_invariants
American mathematician
and symplectic topology). With András I. Stipsicz: 4-manifolds and Kirby calculus, AMS 1999 A new construction of symplectic manifolds, Annals of Mathematics
Robert_Gompf
Study of smooth real-valued functions on manifold and their singularities
the above-mentioned applications, Robion Kirby used Cerf Theory as a key step in justifying the Kirby calculus. A stratification of the complement of an
Cerf_theory
Structure in topology
cork. Gompf, Robert E.; Stipsicz, András I. (1999). 4-manifolds and Kirby calculus. Graduate Studies in Mathematics. Vol. 20. Providence, RI: American
Akbulut_cork
Moduli space of the Seiberg–Witten equations
MR 1339810 Gompf, Robert E.; Stipcisz, András I. (1999). 4-Manifolds and Kirby Calculus. doi:10.1090/gsm/020. ISBN 978-1-4704-7455-3. Nicolaescu, Liviu I. (2000)
Seiberg–Witten_moduli_space
ISBN 978-1-4613-9705-2. Gompf, Robert E.; Stipcisz, András I. (1999). 4-Manifolds and Kirby Calculus. Graduate Studies in Mathematics. Vol. 20. doi:10.1090/gsm/020. ISBN 978-1-4704-7455-3
Freedman_classification
Finite element exterior calculus (FEEC) is a mathematical framework that formulates finite element methods using chain complexes. Its main application
Finite element exterior calculus
Finite_element_exterior_calculus
Graduate-level textbooks in mathematics
Lawrence C. Evans 2010, 2nd ed. 978-0-8218-4974-3 20 4-Manifolds and Kirby Calculus Robert E. Gompf, András I. Stipsicz 1999 978-0-8218-0994-5 21 A Course
Graduate Studies in Mathematics
Graduate_Studies_in_Mathematics
Theorem about natural numbers
Goodstein sequence (as defined below) eventually terminates at 0. Laurence Kirby and Jeff Paris showed in 1982 that Goodstein's theorem is unprovable in
Goodstein's_theorem
UK Parliament constituency (since 1983)
the Metropolitan Borough of Wirral. It includes Greasby, Hoylake, West Kirby, Woodchurch, parts of Upton (with other parts of Upton in the Wallasey constituency)
Wirral_West
Parliamentary constituency in the United Kingdom, 1885 onwards
mortgage by occupants as at the 2011 census across the district. Electoral Calculus categorises the seat as being part of the “Strong Right” demographic, those
Sevenoaks_(constituency)
UK Parliament constituency (1983–2010)
East, Haxby West, Helmsley, Hovingham, Huntington North, Huntington South, Kirby Misperton, Kirkbymoorside, Malton, New Earswick, Norton, Pickering, Rawcliffe
Ryedale_(constituency)
Manifold upon which it is possible to perform calculus
allow one to apply calculus. Any manifold can be described by a collection of charts (atlas). One may then apply ideas from calculus while working within
Differentiable_manifold
UK Parliament constituency (1832–1885, 1983 onwards)
according to Electoral Calculus. 1832–1885: The Hundred of Hemlingford, the County of the City of Coventry, and the Rugby and Kirby Divisions of the Hundred
North Warwickshire and Bedworth
North_Warwickshire_and_Bedworth
Parliamentary constituency in the United Kingdom, 1885 onwards
Horton Kirby, and Longfield. 1997–2010: The Borough of Dartford, and the District of Sevenoaks wards of Fawkham and Hartley, and Horton Kirby. 2010–2024:
Dartford_(constituency)
concerned with numbers, data, collection, quantity, structure, space and calculus. Actuary Demographic marketer Statistician Forensic scientist Gentleman
List of scientific occupations
List_of_scientific_occupations
UK Parliament constituency (since 1983)
2005". Electoral Calculus. Archived from the original on 15 October 2011. Retrieved 18 October 2015. "Election Data 2001". Electoral Calculus. Archived from
Calder_Valley_(constituency)
Family of quantum invariants
{\displaystyle \Bbbk } -linear ribbon category comes equipped with a diagrammatic calculus in which morphisms are represented by certain decorated framed tangle diagrams
Reshetikhin–Turaev_invariant
Topological space that locally resembles Euclidean space
manifolds are differentiable manifolds; their differentiable structure allows calculus to be done. A Riemannian metric on a manifold allows distances and angles
Manifold
UK Parliament constituency (1868–1918, 1974–2024)
1983". Electoral Calculus. Archived from the original on 15 October 2011. Retrieved 18 October 2015. "Election Data 1987". Electoral Calculus. Archived from
Middlesbrough_(constituency)
Fictional comic book villain
published by Marvel Comics. Created by writer Stan Lee and artist Jack Kirby, Space Phantom first appeared in The Avengers vol. 1 #2 (November 1963)
Space_Phantom
Parliamentary constituency in the United Kingdom, 1604–2010
1983". Electoral Calculus. Archived from the original on 15 October 2011. Retrieved 18 October 2015. "Election Data 1987". Electoral Calculus. Archived from
Harwich_(constituency)
Wheeler, Jacob (28 October 2025). "Netherlands Election 2025". Electoral Calculus. Retrieved 28 October 2025. "PVV en D66 met 26 zetels op gelijke hoogte
2025_Dutch_general_election
cardinal numbers) Cantor's theorem (set theory) Church–Rosser theorem (lambda calculus) Compactness theorem (mathematical logic) Conservativity theorem (mathematical
List_of_theorems
English mathematician
of Incrementation") added a new branch to higher mathematics, called "calculus of finite differences". Taylor used this development to determine the form
Brook_Taylor
UK Parliament constituency (1997–2024)
Woodhouse and Swithland, the District of Blaby wards of Ellis, Fairestone, Kirby, Leicester Forest East, the Borough of Hinckley and Bosworth wards of Groby
Charnwood_(constituency)
Principal Japanese breeds of beef cattle
and the skin, brain, horns, and gall bladder removed, and if there is calculus bovis (gallstones), it should be delivered to the state. The Yoro Code
Wagyu
American historian (born 1953)
studies and math courses—world history, U.S. history, algebra, and calculus—at Kirby Hall School and Austin Community College District. His preferred mode
H._W._Brands
British politician (born 1983)
on 22 May 2015. Retrieved 20 May 2015. "Election Data 2015". Electoral Calculus. Archived from the original on 17 October 2015. Retrieved 17 October 2015
Wes_Streeting
American mathematician
Sturm-Liouville theory for partial differential equations and fractional calculus. He is ranked as the leading and most influential researcher in mathematics
George_Karniadakis
Parliamentary constituency in the United Kingdom, 1950 onwards
2010". Electoral Calculus. Archived from the original on 26 July 2013. Retrieved 17 October 2015. "Election Data 2005". Electoral Calculus. Archived from
Brighton Kemptown and Peacehaven
Brighton_Kemptown_and_Peacehaven
Limitative results in mathematical logic
JSTOR 2695030. Zach, Richard (2003). "The Practice of Finitism: Epsilon Calculus and Consistency Proofs in Hilbert's Program" (PDF). Synthese. 137 (1).
Gödel's incompleteness theorems
Gödel's_incompleteness_theorems
Taiwanese-American mathematician
University. Yau was born in 1959 in Taiwan, where he began studying advanced calculus and college algebra in high school. He graduated from National Taiwan University
Horng-Tzer_Yau
American mathematician
George B.; Weir, Maurice D.; Hass, Joel (2014). Thomas' Calculus (13th ed.). Pearson. Kirby, Rob (2020). "Joel Hass: A short biography". Celebratio Mathematica
Joel_Hass
High school in Virginia Beach, Virginia, United States
Chemistry, AP Computer Science, AP Environmental Science, AP Statistics, AP Calculus AB, AP French Language, AP Spanish Language, AP Spanish Literature, AP
Kempsville_High_School
Hard, round-crowned hat with a narrow rolled brim
Timothy "Dum Dum" Dugan (Marvel Comics), Thomson and Thompson and Professor Calculus from The Adventures of Tintin series, and the Riddler (DC Comics). Doctor
Bowler_hat
Facilitation or provision of a prostitute
Anticipating Desistance: Emotions, Conventional Work, and Moral Profitability Calculus". Victims & Offenders. 14 (5): 647–669. doi:10.1080/15564886.2019.1628148
Procuring_(prostitution)
Concept in economics and decision theory
consumption of the good, the idea of "diminishing marginal utility". In calculus notation, the marginal utility of good X is M U x = ∂ U ∂ X {\displaystyle
Utility
J. Catone Bringing Calculus into Discrete Math via the Discrete Derivative 2019 Stanley R. Huddy and Michael A. Jones The Calculus Behind Generic Drug
George_Pólya_Award
Mathematical structure
with some additional mathematical structure that allows for differential calculus on the manifold. If M is already a topological manifold, it is required
Differential_structure
Yes-or-no question that cannot ever be solved by a computer
theorem is a statement about the Ramsey theory of the natural numbers that Kirby and Paris showed is undecidable in Peano arithmetic. Gregory Chaitin produced
Undecidable_problem
Ongoing armed conflict in the Middle East
Patrick (28 November 2023). "A Gaza Truce Aids Both Sides. Until the Calculus Changes". The New York Times. ISSN 0362-4331. Archived from the original
Gaza_war
Charter school
Mathematics Pre-Algebra* Algebra 1 Algebra 2 Geometry Pre-Calculus*/AP Computer Science* AP Calculus BC*/AP Statistics* English American Literature Ancient
Pacific_Collegiate_School
boffin. It is the benign version of the mad scientist stereotype. Prof. Calculus in The Adventures of Tintin series by Hergé Sidney Stratton, played by
List_of_stock_characters
Mathematical logic concept
proof-theoretic ordinal of first-order Peano arithmetic is ε0. Laurence Kirby and Jeff Paris proved in 1982 that Goodstein's theorem cannot be proven
Gentzen's_consistency_proof
Scientist specializing in the field of physics
laboratory experience. Physics students also need training in mathematics (calculus, differential equations, linear algebra, complex analysis, etc.), and in
Physicist
American mathematician (born 1930)
University of Michigan in 1948. Initially, he was placed into an honors calculus sequence taught by Bob Thrall and earned himself A's. However, his sophomore
Stephen_Smale
2025 English local election
seats on the council from 126 to 98. In March 2025, a poll from Electoral Calculus for The Daily Telegraph - of all English local authorities with elections
2025 Durham County Council election
2025_Durham_County_Council_election
Numerical analysis method
Computer Graphics, 25 (4): 3–4, doi:10.1145/127719.122750 Sanderson, Allen R.; Kirby, Robert M.; Johnson, Chris R.; Yang, Lingfa (2006), "Advanced Reaction-Diffusion
Nine-point_stencil
entries all equal to 1 or −1? Hilbert's fifteenth problem: put Schubert calculus on a rigorous foundation. Hilbert's sixteenth problem: what are the possible
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
University Press. ISBN 978-1-107-16841-1. OCLC 1062334376. Paris, J.B.; Kirby, L.A.S. (1978), "Σn-Collection Schemas in Arithmetic", Logic Colloquium
Induction, bounding and least number principles
Induction,_bounding_and_least_number_principles
Greek Stoic philosopher (c.279–c.206 BC)
20th century, with the advances in logic, and the modern propositional calculus, that it became clear that Stoic logic constituted a significant achievement
Chrysippus
Parliamentary constituency in the United Kingdom, 1885 onwards
2015". Electoral Calculus. Archived from the original on 17 October 2015. Retrieved 17 October 2015. "Election Data 2010". Electoral Calculus. Archived from
Rushcliffe_(constituency)
Legal claim of civil wrong
criticised comparative negligence as not encouraging precaution under the calculus of negligence. In response, many states now have a 50% rule where the plaintiff
Tort
Private school in Surrey, British Columbia, Canada
standards), AP courses in these fields, as well as History, Literature and Calculus. Uniquely, the Southridge Senior School implements the Harkness model of
Southridge_School
American historian (born 1951)
Bressoud, David (January 31, 2018). "Why colleges must change how they teach calculus". The Conversation. Retrieved March 27, 2020. "Interview with Nancy A.
Nancy_A._Hewitt
Area of mathematical logic
development of nonstandard analysis, which aims to provide a rigorous calculus of infinitesimals. More recently, the connection between stability and
Model_theory
Concept in classical electromagnetism
issue regarding the continuity equation for electrical charge. In vector calculus, the identity for the divergence of a curl states that the divergence of
Ampère's_circuital_law
Astronomical body that orbits a planet
(2): 24–27. Retrieved 2 August 2025. Hahn, Alexander J. (2020). Basic Calculus of Planetary Orbits and Interplanetary Flight: The Missions of the Voyagers
Natural_satellite
Belgian cartoonist (1907–1983)
the pirate's treasure in the Caribbean, with the character of Professor Calculus being introduced to the series. Following Red Rackham's Treasure, Hergé
Hergé
American physician and gynecologist (1813–1883)
treated by Sims for fistula in 1849. Lavinia Boudurant, 13, had a bladder calculus removed by Sims in 1850. Delia, 23, "Dr. Sims' own servant [slave]", who
J._Marion_Sims
Country within the United Kingdom
developed the ideas of universal gravitation, Newtonian mechanics, and calculus, and Robert Hooke his eponymously named law of elasticity. Other inventions
England
Principle in set theory
Association for Symbolic Logic: 65–77, doi:10.2307/2268862, JSTOR 2268862 Kirby, Laurence (2009), "Finitary Set Theory", Notre Dame J. Formal Logic, 50
Axiom_of_adjunction
Analysis of facts to form a judgment
premises, by use of rules of inference formally those of propositional calculus. For example: X is human and all humans have a face, so X has a face. Induction
Critical_thinking
UK Parliament constituency (since 1974)
Retrieved 4 December 2025. "Seat Details – Leicester West". Electoral Calculus. Retrieved 18 April 2026. "Constituency data: businesses and industries"
Leicester_West
Ship designed for operations near shore
LCS with anti-ship missiles, Navy wargames showed the adversary's risk calculus was radically changed, devoting more reconnaissance assets to trying to
Littoral_combat_ship
UK Parliament constituency (since 1983)
2005". Electoral Calculus. Archived from the original on 15 October 2011. Retrieved 18 October 2015. "Election Data 2001". Electoral Calculus. Archived from
Erewash_(constituency)
Ukrainian–American legal scholar (born 1968)
age. At the age of 9, he was attending university-level mathematics and calculus courses after he was found studying differential equations on his own.
Eugene_Volokh
Parliamentary constituency in the United Kingdom, 1885 onwards
2010". Electoral Calculus. Archived from the original on 26 July 2013. Retrieved 17 October 2015. "Election Data 2005". Electoral Calculus. Archived from
Liverpool_West_Derby
Method for visualizing vector fields
Worcester Polytechnic Institute. Retrieved 2024-07-21. Laidlaw, David H.; Kirby, Robert M.; Davidson, J. Scott; Miller, Timothy S.; da Silva, Marco; Warren
Line_integral_convolution
Public secondary school in Winnetka, Illinois, United States
Placement classes and other college-level classes, such as multivariable calculus and linear algebra, but that level was phased out beginning with the class
New_Trier_High_School
Deputy Prime Minister of the United Kingdom in 2022
July 2022. Retrieved 16 December 2016. "Election Data 2005". Electoral Calculus. Archived from the original on 15 October 2011. Retrieved 18 October 2015
Thérèse_Coffey
Division of typically non-vascular land plants
"Neanderthal behaviour, diet, and disease inferred from ancient DNA in dental calculus" (PDF). Nature. 544 (7650): 357–361. Bibcode:2017Natur.544..357W. doi:10
Moss
UK Parliament constituency (1997–2024)
from the original on 12 November 2019. "Election Data 2015". Electoral Calculus. Archived from the original on 17 October 2015. Retrieved 17 October 2015
Bromley_and_Chislehurst
UK Parliament constituency (since 1997)
2005". Electoral Calculus. Archived from the original on 15 October 2011. Retrieved 18 October 2015. "Election Data 2001". Electoral Calculus. Archived from
South Holland and The Deepings
South_Holland_and_The_Deepings
Science museum in Toronto, Ontario
video game Kirby: Planet Robobot, which also featured activities about the Kirby video game series and a visit by a performer in a full Kirby costume. In
Ontario_Science_Centre
UK Parliament constituency (1918–1945, 1997 onwards)
2005". Electoral Calculus. Archived from the original on 15 October 2011. Retrieved 18 October 2015. "Election Data 2001". Electoral Calculus. Archived from
Hendon_(constituency)
British politician (born 1972)
1997". Electoral Calculus. Archived from the original on 15 October 2011. Retrieved 18 October 2015. "Election Data 2001". Electoral Calculus. Archived from
Steve_Barclay
Alternative form of government or social ordering
economy built on modern computer technology. The Honourable Justice Michael Kirby published a paper in 1998, where he expressed optimism that the then-available
Government_by_algorithm
American mathematician
Project "Perturbation theory for the existence of critical points in the calculus of variations". ProQuest. (PhD dissertation) Profile, Broad Institute,
Jill_P._Mesirov
Parliamentary constituency in the United Kingdom, 1885 onwards
2010". Electoral Calculus. Archived from the original on 26 July 2013. Retrieved 17 October 2015. "Election Data 2005". Electoral Calculus. Archived from
Harborough,_Oadby_and_Wigston
Chinese-American mathematician and poet
While at the IAS, there were two competing methods of geometry: the tensor calculus and the newer differential forms. Chern wrote: I usually like to say that
Shiing-Shen_Chern
Evolutionary theory of social change
survived the most rigorous empirical tests available does not, in the calculus of probability, predict its ability to survive future testing. Karl Popper
Cultural_evolution
Graduate-level textbooks in mathematics
Friedlander 1982-12-01 191 978-0691083179 105 Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. Mariano Giaquinta 1983-11-21
Annals_of_Mathematics_Studies
UK Parliament constituency (since 1997)
News. BBC. Retrieved 30 November 2019. "Election Data 2015". Electoral Calculus. Archived from the original on 17 October 2015. Retrieved 17 October 2015
Cannock_Chase_(constituency)
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