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Kirby, Robion Cromwell

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Author ID: kirby.robion-c Recent zbMATH articles by "Kirby, Robion Cromwell"
Published as: Kirby, Robion; Kirby, R. C.; Kirby, Rob; Kirby, Robion C.
External Links: MacTutor · MGP · Wikidata · GND · IdRef
Documents Indexed: 56 Publications since 1966, including 5 Books
1 Contribution as Editor
Biographic References: 1 Publication

Publications by Year

Citations contained in zbMATH Open

48 Publications have been cited 1,262 times in 1,039 Documents Cited by Year
Foundational essays on topological manifolds, smoothings and triangulations. Zbl 0361.57004
Kirby, Robion C.; Siebenmann, Laurence C.
240
1977
A calculus for framed links in \(S^3\). Zbl 0377.55001
Kirby, Robion
152
1978
The 3-manifold invariants of Witten and Reshetikhin-Turaev for sl\((2,\mathbb{C})\). Zbl 0745.57006
Kirby, Robion; Melvin, Paul
132
1991
Deformations of spaces of imbeddings. Zbl 0214.50303
Edwards, R. D.; Kirby, R. C.
95
1971
The topology of 4-manifolds. Zbl 0668.57001
Kirby, Robion C.
92
1989
On the triangulation of manifolds and the Hauptvermutung. Zbl 0189.54701
Kirby, R. C.; Siebenmann, L. C.
85
1969
Stable homeomorphisms and the annulus conjecture. Zbl 0176.22004
Kirby, R. C.
50
1969
Problems in low dimensional manifold theory. Zbl 0394.57002
Kirby, Rob
49
1978
Branched covers of surfaces in 4-manifolds. Zbl 0421.57002
Akbulut, Selman; Kirby, Robion
38
1980
Dedekind sums, \(\mu\)-invariants and the signature cocycle. Zbl 0809.11027
Kirby, Robion; Melvin, Paul
36
1994
\(Pin\) structures on low-dimensional manifolds. Zbl 0754.57020
Kirby, R. C.; Taylor, L. R.
31
1990
Mazur manifolds. Zbl 0443.57011
Akbulut, Selman; Kirby, Robion
22
1979
Prime knots and concordance. Zbl 0426.57001
Kirby, Robion C.; Lickorish, W. B. Raymond
20
1979
Trisecting 4-manifolds. Zbl 1372.57033
Gay, David T.; Kirby, Robion
20
2016
Handlebody decompositions of complex surfaces. Zbl 0631.57009
Harer, John; Kas, Arnold; Kirby, Robion
19
1986
A potential smooth counterexample in dimension 4 to the Poincaré conjecture, the Schoenflies conjecture, and the Andrews-Curtis conjecture. Zbl 0584.57009
Akbulut, Selman; Kirby, Robion
16
1985
A survey of 4-manifolds through the eyes of surgery. Zbl 0974.57012
Kirby, Robion C.; Taylor, Laurence R.
14
2001
Constructing symplectic forms on 4–manifolds which vanish on circles. Zbl 1054.57027
Gay, David T.; Kirby, Robion
12
2004
On the set of non-locally flat points of a submanifold of codimensional one. Zbl 0185.51603
Kirby, R. C.
11
1968
An exotic involution of \(S^ 4\). Zbl 0465.57013
Akbulut, Selman; Kirby, Robion
10
1979
Constructing Lefschetz-type fibrations on four-manifolds. Zbl 1135.57009
Gay, David T.; Kirby, Robion
9
2007
Slice knots and property R. Zbl 0377.55002
Kirby, Robion; Melvin, Paul
9
1978
Canonical framings for 3-manifolds. Zbl 0947.57020
Kirby, Rob; Melvin, Paul
8
1999
A geometric proof of Rochlin’s theorem. Zbl 0392.57018
Freedman, Michael; Kirby, Robion
8
1978
Normal bundles for codimension 2 locally flat imbeddings. Zbl 0331.57004
Kirby, R. C.; Siebenmann, L. C.
8
1975
Some theorems on topological manifolds. Zbl 0216.45203
Kirby, R. C.; Siebenmann, L. C.
7
1971
Indefinite Morse 2-functions: broken fibrations and generalizations. Zbl 1328.57019
Gay, David T.; Kirby, Robion
7
2015
Local surgery formulas for quantum invariants and the Arf invariant. Zbl 1087.57006
Kirby, Robion; Melvin, Paul
7
2004
Evaluations of the 3-manifolds invariants of Witten and Reshetikhin- Turaev for \(sl(2,C)\). Zbl 0756.57006
Kirby, Robion; Melvin, Paul
5
1990
Fiber-connected, indefinite Morse 2-functions on connected \(n\)-manifolds. Zbl 1256.57024
Gay, David T.; Kirby, Robion C.
5
2011
On the annulus conjecture. Zbl 0151.32902
Kirby, R. C.
4
1966
The union of flat \((n-1)\)-balls is flat in \(R^ n\). Zbl 0157.54603
Kirby, Robion C.
4
1968
Problems in low-dimensional topology. (Edited by Rob Kirby). Zbl 0888.57014
4
1997
Akbulut’s corks and \(h\)-cobordisms of smooth, simply connected 4-manifolds. Zbl 0868.57031
Kirby, Rob
4
1996
Eight faces of the Poincaré homology 3-sphere. Zbl 0511.57008
Kirby, R. C.; Scharlemann, M. G.
4
1982
Cohomotopy sets of 4-manifolds. Zbl 1273.57012
Kirby, Robion; Melvin, Paul; Teichner, Peter
4
2012
Quantum invariants at the sixth root of unity. Zbl 0779.57007
Kirby, Robion; Melvin, Paul; Zhang, Xingru
3
1993
Smoothing locally flat imbeddings of differentiable manifolds. Zbl 0152.22401
Kirby, R. C.
3
1967
Four-manifold theory. (Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference in the Mathematical Sciences on Four-manifold Theory held at Durham, New Hampshire, July 4-10, 1982). Zbl 0549.00018
Kirby, Robion
2
1984
4-manifold problems. Zbl 0558.57004
Kirby, Rob
2
1984
A calculation of \(Pin^ +\) bordism groups. Zbl 0719.55004
Kirby, R. C.; Taylor, L. R.
2
1990
Eight faces of the Poincaré homology 3-sphere. Zbl 0469.57006
Kirby, R. C.; Scharlemann, M. G.
2
1979
Celebratio Mathematica. Zbl 1352.68277
Kirby, Rob
2
2016
Smoothing locally flat imbeddings. Zbl 0138.18803
Kirby, R. C.
1
1966
Some conjectures about four-manifolds. Zbl 0223.57004
Kirby, R. C.
1
1971
A new invariant of 4-manifolds. Zbl 1421.57031
Kirby, Robion; Thompson, Abigail
1
2018
What is …Boy’s surface? Zbl 1151.53306
Kirby, Rob
1
2007
A curious category which equals TOP. Zbl 0315.57003
Kirby, R. C.; Scharlemann, M. G.
1
1975
A new invariant of 4-manifolds. Zbl 1421.57031
Kirby, Robion; Thompson, Abigail
1
2018
Trisecting 4-manifolds. Zbl 1372.57033
Gay, David T.; Kirby, Robion
20
2016
Celebratio Mathematica. Zbl 1352.68277
Kirby, Rob
2
2016
Indefinite Morse 2-functions: broken fibrations and generalizations. Zbl 1328.57019
Gay, David T.; Kirby, Robion
7
2015
Cohomotopy sets of 4-manifolds. Zbl 1273.57012
Kirby, Robion; Melvin, Paul; Teichner, Peter
4
2012
Fiber-connected, indefinite Morse 2-functions on connected \(n\)-manifolds. Zbl 1256.57024
Gay, David T.; Kirby, Robion C.
5
2011
Constructing Lefschetz-type fibrations on four-manifolds. Zbl 1135.57009
Gay, David T.; Kirby, Robion
9
2007
What is …Boy’s surface? Zbl 1151.53306
Kirby, Rob
1
2007
Constructing symplectic forms on 4–manifolds which vanish on circles. Zbl 1054.57027
Gay, David T.; Kirby, Robion
12
2004
Local surgery formulas for quantum invariants and the Arf invariant. Zbl 1087.57006
Kirby, Robion; Melvin, Paul
7
2004
A survey of 4-manifolds through the eyes of surgery. Zbl 0974.57012
Kirby, Robion C.; Taylor, Laurence R.
14
2001
Canonical framings for 3-manifolds. Zbl 0947.57020
Kirby, Rob; Melvin, Paul
8
1999
Problems in low-dimensional topology. (Edited by Rob Kirby). Zbl 0888.57014
4
1997
Akbulut’s corks and \(h\)-cobordisms of smooth, simply connected 4-manifolds. Zbl 0868.57031
Kirby, Rob
4
1996
Dedekind sums, \(\mu\)-invariants and the signature cocycle. Zbl 0809.11027
Kirby, Robion; Melvin, Paul
36
1994
Quantum invariants at the sixth root of unity. Zbl 0779.57007
Kirby, Robion; Melvin, Paul; Zhang, Xingru
3
1993
The 3-manifold invariants of Witten and Reshetikhin-Turaev for sl\((2,\mathbb{C})\). Zbl 0745.57006
Kirby, Robion; Melvin, Paul
132
1991
\(Pin\) structures on low-dimensional manifolds. Zbl 0754.57020
Kirby, R. C.; Taylor, L. R.
31
1990
Evaluations of the 3-manifolds invariants of Witten and Reshetikhin- Turaev for \(sl(2,C)\). Zbl 0756.57006
Kirby, Robion; Melvin, Paul
5
1990
A calculation of \(Pin^ +\) bordism groups. Zbl 0719.55004
Kirby, R. C.; Taylor, L. R.
2
1990
The topology of 4-manifolds. Zbl 0668.57001
Kirby, Robion C.
92
1989
Handlebody decompositions of complex surfaces. Zbl 0631.57009
Harer, John; Kas, Arnold; Kirby, Robion
19
1986
A potential smooth counterexample in dimension 4 to the Poincaré conjecture, the Schoenflies conjecture, and the Andrews-Curtis conjecture. Zbl 0584.57009
Akbulut, Selman; Kirby, Robion
16
1985
Four-manifold theory. (Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference in the Mathematical Sciences on Four-manifold Theory held at Durham, New Hampshire, July 4-10, 1982). Zbl 0549.00018
Kirby, Robion
2
1984
4-manifold problems. Zbl 0558.57004
Kirby, Rob
2
1984
Eight faces of the Poincaré homology 3-sphere. Zbl 0511.57008
Kirby, R. C.; Scharlemann, M. G.
4
1982
Branched covers of surfaces in 4-manifolds. Zbl 0421.57002
Akbulut, Selman; Kirby, Robion
38
1980
Mazur manifolds. Zbl 0443.57011
Akbulut, Selman; Kirby, Robion
22
1979
Prime knots and concordance. Zbl 0426.57001
Kirby, Robion C.; Lickorish, W. B. Raymond
20
1979
An exotic involution of \(S^ 4\). Zbl 0465.57013
Akbulut, Selman; Kirby, Robion
10
1979
Eight faces of the Poincaré homology 3-sphere. Zbl 0469.57006
Kirby, R. C.; Scharlemann, M. G.
2
1979
A calculus for framed links in \(S^3\). Zbl 0377.55001
Kirby, Robion
152
1978
Problems in low dimensional manifold theory. Zbl 0394.57002
Kirby, Rob
49
1978
Slice knots and property R. Zbl 0377.55002
Kirby, Robion; Melvin, Paul
9
1978
A geometric proof of Rochlin’s theorem. Zbl 0392.57018
Freedman, Michael; Kirby, Robion
8
1978
Foundational essays on topological manifolds, smoothings and triangulations. Zbl 0361.57004
Kirby, Robion C.; Siebenmann, Laurence C.
240
1977
Normal bundles for codimension 2 locally flat imbeddings. Zbl 0331.57004
Kirby, R. C.; Siebenmann, L. C.
8
1975
A curious category which equals TOP. Zbl 0315.57003
Kirby, R. C.; Scharlemann, M. G.
1
1975
Deformations of spaces of imbeddings. Zbl 0214.50303
Edwards, R. D.; Kirby, R. C.
95
1971
Some theorems on topological manifolds. Zbl 0216.45203
Kirby, R. C.; Siebenmann, L. C.
7
1971
Some conjectures about four-manifolds. Zbl 0223.57004
Kirby, R. C.
1
1971
On the triangulation of manifolds and the Hauptvermutung. Zbl 0189.54701
Kirby, R. C.; Siebenmann, L. C.
85
1969
Stable homeomorphisms and the annulus conjecture. Zbl 0176.22004
Kirby, R. C.
50
1969
On the set of non-locally flat points of a submanifold of codimensional one. Zbl 0185.51603
Kirby, R. C.
11
1968
The union of flat \((n-1)\)-balls is flat in \(R^ n\). Zbl 0157.54603
Kirby, Robion C.
4
1968
Smoothing locally flat imbeddings of differentiable manifolds. Zbl 0152.22401
Kirby, R. C.
3
1967
On the annulus conjecture. Zbl 0151.32902
Kirby, R. C.
4
1966
Smoothing locally flat imbeddings. Zbl 0138.18803
Kirby, R. C.
1
1966
all top 5

Cited by 978 Authors

18 Farrell, F. Thomas
13 Kirby, Robion Cromwell
12 Kwasik, Sławomir
12 Le, Thang Tu Quoc
11 Livingston, Charles
10 Jones, Lowell Edwin
9 Akbulut, Selman
9 Gay, David T.
9 Ruberman, Daniel
9 Siebenmann, Laurence C.
9 Stoimenow, Alexander
8 Cavicchioli, Alberto
8 Gilmer, Patrick M.
8 Gompf, Robert E.
8 Murakami, Hitoshi
8 Weinberger, Shmuel
7 Cochran, Thomas (Tim) Daniel
7 Ferry, Steven C.
7 Garoufalidis, Stavros
7 Kauffman, Louis Hirsch
7 Khan, Qayum
7 Melvin, Paul M.
7 Quinn, Frank S.
7 Rybicki, Tomasz
7 Weiss, Michael S.
6 Bryant, John Logan
6 Cha, Jae Choon
6 Crowley, Diarmuid John
6 Lisca, Paolo
6 Ogasa, Eiji
6 Ray, Arunima
6 Repovš, Dušan D.
6 Schultz, Reinhard E.
6 Stern, Ronald John
6 Stipsicz, András I.
6 Teichner, Peter
6 Williams, Bruce
6 Yamada, Yuichi
5 Cappell, Sylvain E.
5 Chapman, Thomas Ashland
5 Costantino, Francesco
5 Daverman, Robert J.
5 Freedman, Michael Hartley
5 Grines, Vyacheslav Zigmundovich
5 Habiro, Kazuo
5 Hambleton, Ian
5 Kreck, Matthias
5 Ohtsuki, Tomotada
5 Saveliev, Nikolai
5 Shiota, Masahiro
5 Spaggiari, Fulvia
5 Takata, Toshie
5 Taylor, Laurence Robert
5 Turaev, Vladimir G.
4 Auckly, David R.
4 Benedetti, Bruno
4 Burghelea, Dan
4 Calegari, Danny Matthew Cornelius
4 Casali, Maria Rita
4 Chen, Qi
4 Gauld, David B.
4 Geer, Nathan
4 Gukov, Sergei
4 Hayano, Kenta
4 Hegenbarth, Friedrich
4 Hillman, Jonathan Arthur
4 Hsiang, Wu-Chung
4 Hughes, C. Bruce
4 Pedersen, Erik Kjær
4 Lashof, Richard K.
4 Lawrence, Ruth J.
4 Levine, Jerome P.
4 Macko, Tibor
4 Medvedev, Vladislav Sergeevich
4 Meier, Jeffrey
4 Murakami, Jun
4 Nakamura, Nobuhiro
4 Patureau-Mirand, Bertrand
4 Powell, Mark
4 Sati, Hisham
4 Sawin, Stephen F.
4 Scharlemann, Martin G.
4 Sozen, Yasar
4 Walker, Kevin
4 Yasui, Kouichi
3 Adiprasito, Karim Alexander
3 Alpern, Steve
3 Aßelmeyer-Maluga, Torsten
3 Ayala, David
3 Baykur, Refik İnanç
3 Beliakova, Anna
3 Burton, Benjamin A.
3 Cristofori, Paola
3 Francis, John
3 Frohman, Charles D.
3 Funar, Louis
3 Gagliardi, Carlo
3 Gómez Larrañaga, José Carlos
3 González Acuña, Francisco Javier
3 Grove, Karsten
...and 878 more Authors
all top 5

Cited in 190 Serials

86 Topology and its Applications
76 Transactions of the American Mathematical Society
57 Proceedings of the American Mathematical Society
57 Journal of Knot Theory and its Ramifications
55 Algebraic & Geometric Topology
51 Geometry & Topology
46 Inventiones Mathematicae
26 Communications in Mathematical Physics
26 Bulletin of the American Mathematical Society
23 Mathematical Proceedings of the Cambridge Philosophical Society
22 Mathematische Annalen
21 Advances in Mathematics
19 Bulletin of the American Mathematical Society. New Series
16 Geometriae Dedicata
15 Mathematische Zeitschrift
14 Journal of Mathematical Physics
14 Journal of Topology
13 Compositio Mathematica
13 Duke Mathematical Journal
12 International Journal of Mathematics
11 Journal of High Energy Physics
8 \(K\)-Theory
7 Journal of Geometry and Physics
7 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
7 Journal of Pure and Applied Algebra
7 Manuscripta Mathematica
7 Osaka Journal of Mathematics
7 Journal of the American Mathematical Society
7 Quantum Topology
6 Communications on Pure and Applied Mathematics
6 Proceedings of the Steklov Institute of Mathematics
5 Bulletin of the Australian Mathematical Society
5 Bulletin of the London Mathematical Society
5 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
5 Experimental Mathematics
5 Annals of Mathematics. Second Series
4 Letters in Mathematical Physics
4 Rocky Mountain Journal of Mathematics
4 Annales de l’Institut Fourier
4 Memoirs of the American Mathematical Society
4 Proceedings of the Edinburgh Mathematical Society. Series II
4 Ergodic Theory and Dynamical Systems
4 International Journal of Algebra and Computation
4 The Journal of Geometric Analysis
4 Comptes Rendus. Mathématique. Académie des Sciences, Paris
4 Journal of Topology and Analysis
3 Communications in Algebra
3 Chaos, Solitons and Fractals
3 The Mathematical Intelligencer
3 Acta Mathematica
3 Acta Mathematica Vietnamica
3 Cahiers de Topologie et Géométrie Différentielle Catégoriques
3 Publications Mathématiques
3 Journal of the London Mathematical Society. Second Series
3 Journal of the Mathematical Society of Japan
3 Journal of Number Theory
3 Journal für die Reine und Angewandte Mathematik
3 Michigan Mathematical Journal
3 Publications of the Research Institute for Mathematical Sciences, Kyoto University
3 Tohoku Mathematical Journal. Second Series
3 European Journal of Combinatorics
3 Journal of Mathematical Sciences (New York)
3 Selecta Mathematica. New Series
3 Conformal Geometry and Dynamics
3 Acta Mathematica Sinica. English Series
3 Journal of the Australian Mathematical Society
3 Journal of Homotopy and Related Structures
2 Israel Journal of Mathematics
2 Journal of Mathematical Analysis and Applications
2 Mathematical Notes
2 Nuclear Physics. B
2 Periodica Mathematica Hungarica
2 Ukrainian Mathematical Journal
2 Archiv der Mathematik
2 Functional Analysis and its Applications
2 Fundamenta Mathematicae
2 Glasgow Mathematical Journal
2 International Journal of Mathematics and Mathematical Sciences
2 Mathematika
2 Monatshefte für Mathematik
2 Pacific Journal of Mathematics
2 Proceedings of the London Mathematical Society. Third Series
2 Results in Mathematics
2 Differential Geometry and its Applications
2 L’Enseignement Mathématique. 2e Série
2 Proceedings of the National Academy of Sciences of the United States of America
2 Chinese Science Bulletin
2 Calculus of Variations and Partial Differential Equations
2 St. Petersburg Mathematical Journal
2 Journal of the European Mathematical Society (JEMS)
2 Journal of Algebra and its Applications
2 Groups, Geometry, and Dynamics
2 Science China. Mathematics
2 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
2 Forum of Mathematics, Sigma
2 Open Mathematics
2 Journal de l’École Polytechnique – Mathématiques
1 Modern Physics Letters A
1 Archive for Rational Mechanics and Analysis
1 General Relativity and Gravitation
...and 90 more Serials
all top 5

Cited in 48 Fields

863 Manifolds and cell complexes (57-XX)
128 Algebraic topology (55-XX)
111 Differential geometry (53-XX)
82 Global analysis, analysis on manifolds (58-XX)
81 Quantum theory (81-XX)
50 Algebraic geometry (14-XX)
50 Group theory and generalizations (20-XX)
47 General topology (54-XX)
43 Category theory; homological algebra (18-XX)
41 Dynamical systems and ergodic theory (37-XX)
40 Nonassociative rings and algebras (17-XX)
33 Several complex variables and analytic spaces (32-XX)
25 Number theory (11-XX)
21 Topological groups, Lie groups (22-XX)
17 Associative rings and algebras (16-XX)
17 \(K\)-theory (19-XX)
17 Relativity and gravitational theory (83-XX)
15 Combinatorics (05-XX)
14 Functions of a complex variable (30-XX)
11 Partial differential equations (35-XX)
10 Computer science (68-XX)
10 Statistical mechanics, structure of matter (82-XX)
9 Measure and integration (28-XX)
9 Functional analysis (46-XX)
8 History and biography (01-XX)
7 Convex and discrete geometry (52-XX)
6 Real functions (26-XX)
6 Approximations and expansions (41-XX)
6 Geometry (51-XX)
6 Biology and other natural sciences (92-XX)
4 Special functions (33-XX)
3 Order, lattices, ordered algebraic structures (06-XX)
3 Linear and multilinear algebra; matrix theory (15-XX)
3 Potential theory (31-XX)
3 Calculus of variations and optimal control; optimization (49-XX)
2 Mathematical logic and foundations (03-XX)
2 Field theory and polynomials (12-XX)
2 Ordinary differential equations (34-XX)
2 Probability theory and stochastic processes (60-XX)
2 Statistics (62-XX)
1 General and overarching topics; collections (00-XX)
1 Commutative algebra (13-XX)
1 Harmonic analysis on Euclidean spaces (42-XX)
1 Operator theory (47-XX)
1 Mechanics of deformable solids (74-XX)
1 Operations research, mathematical programming (90-XX)
1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
1 Information and communication theory, circuits (94-XX)

Citations by Year

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