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Kirby, Robion Cromwell

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: 57 Publications since 1966, including 4 Books and 1 Additional arXiv Preprint
2 Contributions as Editor
Biographic References: 1 Publication
Co-Authors: 23 Co-Authors with 39 Joint Publications
442 Co-Co-Authors

Publications by Year

Citations contained in zbMATH Open

52 Publications have been cited 1,690 times in 1,378 Documents Cited by Year
Foundational essays on topological manifolds, smoothings and triangulations. Zbl 0361.57004
Kirby, Robion C.; Siebenmann, Laurence C.
292
1977
A calculus for framed links in \(S^3\). Zbl 0377.55001
Kirby, Robion
175
1978
The 3-manifold invariants of Witten and Reshetikhin-Turaev for sl\((2,\mathbb{C})\). Zbl 0745.57006
Kirby, Robion; Melvin, Paul
160
1991
The topology of 4-manifolds. Zbl 0668.57001
Kirby, Robion C.
139
1989
Deformations of spaces of imbeddings. Zbl 0214.50303
Edwards, R. D.; Kirby, R. C.
113
1971
On the triangulation of manifolds and the Hauptvermutung. Zbl 0189.54701
Kirby, R. C.; Siebenmann, L. C.
102
1969
Problems in low-dimensional topology. (Edited by Rob Kirby). Zbl 0888.57014
98
1997
Problems in low dimensional manifold theory. Zbl 0394.57002
Kirby, Rob
87
1978
Trisecting 4-manifolds. Zbl 1372.57033
Gay, David T.; Kirby, Robion
69
2016
Stable homeomorphisms and the annulus conjecture. Zbl 0176.22004
Kirby, R. C.
57
1969
Branched covers of surfaces in 4-manifolds. Zbl 0421.57002
Akbulut, Selman; Kirby, Robion
54
1980
\(Pin\) structures on low-dimensional manifolds. Zbl 0754.57020
Kirby, R. C.; Taylor, L. R.
52
1990
Dedekind sums, \(\mu\)-invariants and the signature cocycle. Zbl 0809.11027
Kirby, Robion; Melvin, Paul
47
1994
Mazur manifolds. Zbl 0443.57011
Akbulut, Selman; Kirby, Robion
32
1979
Prime knots and concordance. Zbl 0426.57001
Kirby, Robion C.; Lickorish, W. B. Raymond
25
1979
Handlebody decompositions of complex surfaces. Zbl 0631.57009
Harer, John; Kas, Arnold; Kirby, Robion
23
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
22
1985
A geometric proof of Rochlin’s theorem. Zbl 0392.57018
Freedman, Michael; Kirby, Robion
18
1978
A survey of 4-manifolds through the eyes of surgery. Zbl 0974.57012
Kirby, Robion C.; Taylor, Laurence R.
17
2001
Constructing symplectic forms on 4–manifolds which vanish on circles. Zbl 1054.57027
Gay, David T.; Kirby, Robion
15
2004
An exotic involution of \(S^ 4\). Zbl 0465.57013
Akbulut, Selman; Kirby, Robion
13
1979
Eight faces of the Poincaré homology 3-sphere. Zbl 0469.57006
Kirby, R. C.; Scharlemann, M. G.
13
1979
Constructing Lefschetz-type fibrations on four-manifolds. Zbl 1135.57009
Gay, David T.; Kirby, Robion
12
2007
Indefinite Morse 2-functions: broken fibrations and generalizations. Zbl 1328.57019
Gay, David T.; Kirby, Robion
12
2015
Canonical framings for 3-manifolds. Zbl 0947.57020
Kirby, Rob; Melvin, Paul
11
1999
On the set of non-locally flat points of a submanifold of codimensional one. Zbl 0185.51603
Kirby, R. C.
11
1968
Normal bundles for codimension 2 locally flat imbeddings. Zbl 0331.57004
Kirby, R. C.; Siebenmann, L. C.
10
1975
Slice knots and property R. Zbl 0377.55002
Kirby, Robion; Melvin, Paul
10
1978
Local surgery formulas for quantum invariants and the Arf invariant. Zbl 1087.57006
Kirby, Robion; Melvin, Paul
9
2004
A calculation of \(Pin^ +\) bordism groups. Zbl 0719.55004
Kirby, R. C.; Taylor, L. R.
7
1990
Some theorems on topological manifolds. Zbl 0216.45203
Kirby, R. C.; Siebenmann, L. C.
7
1971
Cohomotopy sets of 4-manifolds. Zbl 1273.57012
Kirby, Robion; Melvin, Paul; Teichner, Peter
7
2012
Fiber-connected, indefinite Morse 2-functions on connected \(n\)-manifolds. Zbl 1256.57024
Gay, David T.; Kirby, Robion C.
7
2011
4-manifold problems. Zbl 0558.57004
Kirby, Rob
6
1984
Evaluations of the 3-manifolds invariants of Witten and Reshetikhin- Turaev for \(sl(2,C)\). Zbl 0756.57006
Kirby, Robion; Melvin, Paul
6
1990
Group trisections and smooth 4-manifolds. Zbl 1404.57001
Abrams, Aaron; Gay, David; Kirby, Robion
5
2018
A new invariant of 4-manifolds. Zbl 1421.57031
Kirby, Robion; Thompson, Abigail
5
2018
Celebratio Mathematica. Zbl 1352.68277
Kirby, Rob
5
2016
Quantum invariants at the sixth root of unity. Zbl 0779.57007
Kirby, Robion; Melvin, Paul; Zhang, Xingru
5
1993
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
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
Memories of Vaughan Jones. Zbl 1480.01028
Bisch, Dietmar; Evans, David E.; Kirby, Robion; Popa, Sorin
3
2021
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
2
1984
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
Reconstructing 4-manifolds from Morse 2-functions. Zbl 1267.57020
Gay, David; Kirby, Robion
1
2012
Trisections of 4-manifolds. Zbl 1421.57030
Kirby, Robion
1
2018
Some conjectures about four-manifolds. Zbl 0223.57004
Kirby, R. C.
1
1971
Smoothing locally flat imbeddings. Zbl 0138.18803
Kirby, R. C.
1
1966
Memories of Vaughan Jones. Zbl 1480.01028
Bisch, Dietmar; Evans, David E.; Kirby, Robion; Popa, Sorin
3
2021
Group trisections and smooth 4-manifolds. Zbl 1404.57001
Abrams, Aaron; Gay, David; Kirby, Robion
5
2018
A new invariant of 4-manifolds. Zbl 1421.57031
Kirby, Robion; Thompson, Abigail
5
2018
Trisections of 4-manifolds. Zbl 1421.57030
Kirby, Robion
1
2018
Trisecting 4-manifolds. Zbl 1372.57033
Gay, David T.; Kirby, Robion
69
2016
Celebratio Mathematica. Zbl 1352.68277
Kirby, Rob
5
2016
Indefinite Morse 2-functions: broken fibrations and generalizations. Zbl 1328.57019
Gay, David T.; Kirby, Robion
12
2015
Cohomotopy sets of 4-manifolds. Zbl 1273.57012
Kirby, Robion; Melvin, Paul; Teichner, Peter
7
2012
Reconstructing 4-manifolds from Morse 2-functions. Zbl 1267.57020
Gay, David; Kirby, Robion
1
2012
Fiber-connected, indefinite Morse 2-functions on connected \(n\)-manifolds. Zbl 1256.57024
Gay, David T.; Kirby, Robion C.
7
2011
Constructing Lefschetz-type fibrations on four-manifolds. Zbl 1135.57009
Gay, David T.; Kirby, Robion
12
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
15
2004
Local surgery formulas for quantum invariants and the Arf invariant. Zbl 1087.57006
Kirby, Robion; Melvin, Paul
9
2004
A survey of 4-manifolds through the eyes of surgery. Zbl 0974.57012
Kirby, Robion C.; Taylor, Laurence R.
17
2001
Canonical framings for 3-manifolds. Zbl 0947.57020
Kirby, Rob; Melvin, Paul
11
1999
Problems in low-dimensional topology. (Edited by Rob Kirby). Zbl 0888.57014
98
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
47
1994
Quantum invariants at the sixth root of unity. Zbl 0779.57007
Kirby, Robion; Melvin, Paul; Zhang, Xingru
5
1993
The 3-manifold invariants of Witten and Reshetikhin-Turaev for sl\((2,\mathbb{C})\). Zbl 0745.57006
Kirby, Robion; Melvin, Paul
160
1991
\(Pin\) structures on low-dimensional manifolds. Zbl 0754.57020
Kirby, R. C.; Taylor, L. R.
52
1990
A calculation of \(Pin^ +\) bordism groups. Zbl 0719.55004
Kirby, R. C.; Taylor, L. R.
7
1990
Evaluations of the 3-manifolds invariants of Witten and Reshetikhin- Turaev for \(sl(2,C)\). Zbl 0756.57006
Kirby, Robion; Melvin, Paul
6
1990
The topology of 4-manifolds. Zbl 0668.57001
Kirby, Robion C.
139
1989
Handlebody decompositions of complex surfaces. Zbl 0631.57009
Harer, John; Kas, Arnold; Kirby, Robion
23
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
22
1985
4-manifold problems. Zbl 0558.57004
Kirby, Rob
6
1984
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
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
54
1980
Mazur manifolds. Zbl 0443.57011
Akbulut, Selman; Kirby, Robion
32
1979
Prime knots and concordance. Zbl 0426.57001
Kirby, Robion C.; Lickorish, W. B. Raymond
25
1979
An exotic involution of \(S^ 4\). Zbl 0465.57013
Akbulut, Selman; Kirby, Robion
13
1979
Eight faces of the Poincaré homology 3-sphere. Zbl 0469.57006
Kirby, R. C.; Scharlemann, M. G.
13
1979
A calculus for framed links in \(S^3\). Zbl 0377.55001
Kirby, Robion
175
1978
Problems in low dimensional manifold theory. Zbl 0394.57002
Kirby, Rob
87
1978
A geometric proof of Rochlin’s theorem. Zbl 0392.57018
Freedman, Michael; Kirby, Robion
18
1978
Slice knots and property R. Zbl 0377.55002
Kirby, Robion; Melvin, Paul
10
1978
Foundational essays on topological manifolds, smoothings and triangulations. Zbl 0361.57004
Kirby, Robion C.; Siebenmann, Laurence C.
292
1977
Normal bundles for codimension 2 locally flat imbeddings. Zbl 0331.57004
Kirby, R. C.; Siebenmann, L. C.
10
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.
113
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.
102
1969
Stable homeomorphisms and the annulus conjecture. Zbl 0176.22004
Kirby, R. C.
57
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 1,310 Authors

20 Farrell, F. Thomas
13 Kirby, Robion Cromwell
13 Kwasik, Sławomir
13 Livingston, Charles
13 Ruberman, Daniel
12 Kauffman, Louis Hirsch
12 Le, Thang Tu Quoc
12 Ray, Arunima
10 Cavicchioli, Alberto
10 Jones, Lowell Edwin
10 Meier, Jeffrey
10 Murakami, Hitoshi
10 Powell, Mark
10 Stoimenow, Alexander
9 Akbulut, Selman
9 Cochran, Thomas (Tim) Daniel
9 Gay, David T.
9 Gompf, Robert E.
9 Ogasa, Eiji
9 Siebenmann, Laurence C.
9 Weiss, Michael S.
8 Crowley, Diarmuid John
8 Gilmer, Patrick M.
8 Melvin, Paul M.
8 Rybicki, Tomasz
8 Saveliev, Nikolai
8 Stipsicz, András I.
8 Teichner, Peter
8 Weinberger, Shmuel
7 Auckly, David R.
7 Cha, Jae Choon
7 Ferry, Steven C.
7 Garoufalidis, Stavros
7 Grines, Vyacheslav Zigmundovich
7 Hambleton, Ian
7 Khan, Qayum
7 Lisca, Paolo
7 Miller, Allison N.
7 Miller, Maggie
7 Quinn, Frank S.
7 Repovš, Dušan D.
7 Spaggiari, Fulvia
6 Baykur, Refik İnanç
6 Bryant, John Logan
6 Costantino, Francesco
6 Habiro, Kazuo
6 Kupers, Alexander
6 Lambert-Cole, Peter
6 Land, Markus
6 Mann, Kathryn
6 Nakamura, Nobuhiro
6 Putrov, Pavel
6 Schultz, Reinhard E.
6 Spreer, Jonathan
6 Stern, Ronald John
6 Williams, Bruce
6 Yamada, Yuichi
6 Zupan, Alexander
5 Cappell, Sylvain E.
5 Casali, Maria Rita
5 Chapman, Thomas Ashland
5 Daverman, Robert J.
5 Du, Kun
5 Etnyre, John B.
5 Freedman, Michael Hartley
5 Friedl, Stefan
5 Gukov, Sergei
5 Hegenbarth, Friedrich
5 Hillman, Jonathan Arthur
5 Kasprowski, Daniel
5 Kreck, Matthias
5 Lidman, Tye
5 Macko, Tibor
5 Ohtsuki, Tomotada
5 Park, Junghwan
5 Randal-Williams, Oscar
5 Sati, Hisham
5 Scharlemann, Martin G.
5 Shiota, Masahiro
5 Sozen, Yasar
5 Takata, Toshie
5 Taylor, Laurence Robert
5 Tillmann, Stephan
5 Turaev, Vladimir Georgievich
5 Vassiliev, Dmitri G.
5 Yasui, Kouichi
5 Zuddas, Daniele
4 Benedetti, Bruno
4 Burghelea, Dan
4 Burton, Benjamin A.
4 Calegari, Danny Matthew Cornelius
4 Chen, Qi
4 Conway, Anthony
4 Cristofori, Paola
4 Gauld, David B.
4 Geer, Nathan
4 Guadagnini, Enore
4 Gurevich, Elena Yakovlevna
4 Hayano, Kenta
4 Hsiang, Wu-Chung
...and 1,210 more Authors
all top 5

Cited in 222 Serials

109 Topology and its Applications
85 Transactions of the American Mathematical Society
76 Journal of Knot Theory and its Ramifications
76 Algebraic & Geometric Topology
64 Geometry & Topology
61 Proceedings of the American Mathematical Society
48 Inventiones Mathematicae
37 Journal of Topology
33 Communications in Mathematical Physics
26 Bulletin of the American Mathematical Society
25 Mathematische Annalen
24 Advances in Mathematics
23 Mathematical Proceedings of the Cambridge Philosophical Society
23 Bulletin of the American Mathematical Society. New Series
22 Geometriae Dedicata
17 Journal of Mathematical Physics
17 Mathematische Zeitschrift
16 Journal of High Energy Physics
15 Duke Mathematical Journal
14 International Journal of Mathematics
13 Compositio Mathematica
11 Pacific Journal of Mathematics
11 Quantum Topology
10 Journal of Geometry and Physics
10 Bulletin of the London Mathematical Society
10 Journal of Pure and Applied Algebra
10 Journal of the American Mathematical Society
9 Journal of the London Mathematical Society. Second Series
8 Letters in Mathematical Physics
8 Michigan Mathematical Journal
8 Osaka Journal of Mathematics
8 \(K\)-Theory
8 Experimental Mathematics
8 Journal of the European Mathematical Society (JEMS)
8 Proceedings of the Steklov Institute of Mathematics
7 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
7 Manuscripta Mathematica
7 Journal of Topology and Analysis
6 Communications on Pure and Applied Mathematics
6 Annales de l’Institut Fourier
6 Annals of Mathematics. Second Series
6 Comptes Rendus. Mathématique. Académie des Sciences, Paris
5 Bulletin of the Australian Mathematical Society
5 Nuclear Physics. B
5 Rocky Mountain Journal of Mathematics
5 Canadian Journal of Mathematics
5 Journal für die Reine und Angewandte Mathematik
5 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
5 Oberwolfach Reports
5 Winter Braids Lecture Notes
4 Israel Journal of Mathematics
4 Memoirs of the American Mathematical Society
4 Proceedings of the Edinburgh Mathematical Society. Series II
4 Proceedings of the London Mathematical Society. Third Series
4 European Journal of Combinatorics
4 Ergodic Theory and Dynamical Systems
4 Forum Mathematicum
4 International Journal of Algebra and Computation
4 The Journal of Geometric Analysis
4 L’Enseignement Mathématique. 2e Série
4 Expositiones Mathematicae
4 Selecta Mathematica. New Series
4 Groups, Geometry, and Dynamics
4 Science China. Mathematics
4 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
4 Forum of Mathematics, Sigma
4 EMS Surveys in Mathematical Sciences
3 Communications in Algebra
3 Chaos, Solitons and Fractals
3 The Mathematical Intelligencer
3 Acta Mathematica
3 Acta Mathematica Vietnamica
3 Archiv der Mathematik
3 Cahiers de Topologie et Géométrie Différentielle Catégoriques
3 Glasgow Mathematical Journal
3 Publications Mathématiques
3 Journal of Differential Geometry
3 Journal of the Mathematical Society of Japan
3 Journal of Number Theory
3 Publications of the Research Institute for Mathematical Sciences, Kyoto University
3 Results in Mathematics
3 Tôhoku Mathematical Journal. Second Series
3 Differential Geometry and its Applications
3 Journal of Mathematical Sciences (New York)
3 The New York Journal of Mathematics
3 Conformal Geometry and Dynamics
3 Acta Mathematica Sinica. English Series
3 Annales Henri Poincaré
3 Journal of the Australian Mathematical Society
3 Journal of Homotopy and Related Structures
3 Proceedings of the American Mathematical Society. Series B
3 Transactions of the American Mathematical Society. Series B
2 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV)
2 Journal of Mathematical Analysis and Applications
2 Mathematical Notes
2 Periodica Mathematica Hungarica
2 Ukrainian Mathematical Journal
2 Reviews in Mathematical Physics
2 Archivum Mathematicum
2 Functional Analysis and its Applications
...and 122 more Serials
all top 5

Cited in 50 Fields

1,138 Manifolds and cell complexes (57-XX)
169 Algebraic topology (55-XX)
137 Differential geometry (53-XX)
116 Quantum theory (81-XX)
102 Global analysis, analysis on manifolds (58-XX)
70 Group theory and generalizations (20-XX)
69 Algebraic geometry (14-XX)
55 General topology (54-XX)
50 Category theory; homological algebra (18-XX)
46 Dynamical systems and ergodic theory (37-XX)
45 Nonassociative rings and algebras (17-XX)
44 Several complex variables and analytic spaces (32-XX)
38 Number theory (11-XX)
27 Topological groups, Lie groups (22-XX)
24 Relativity and gravitational theory (83-XX)
23 Combinatorics (05-XX)
21 \(K\)-theory (19-XX)
20 Associative rings and algebras (16-XX)
18 History and biography (01-XX)
16 Statistical mechanics, structure of matter (82-XX)
15 Functions of a complex variable (30-XX)
15 Functional analysis (46-XX)
13 Computer science (68-XX)
12 Convex and discrete geometry (52-XX)
11 Partial differential equations (35-XX)
9 General and overarching topics; collections (00-XX)
9 Measure and integration (28-XX)
9 Geometry (51-XX)
6 Real functions (26-XX)
6 Approximations and expansions (41-XX)
5 Mathematical logic and foundations (03-XX)
5 Linear and multilinear algebra; matrix theory (15-XX)
4 Special functions (33-XX)
4 Calculus of variations and optimal control; optimization (49-XX)
3 Order, lattices, ordered algebraic structures (06-XX)
3 Potential theory (31-XX)
3 Ordinary differential equations (34-XX)
3 Statistics (62-XX)
2 Field theory and polynomials (12-XX)
2 Commutative algebra (13-XX)
2 Operator theory (47-XX)
2 Probability theory and stochastic processes (60-XX)
2 Mechanics of particles and systems (70-XX)
2 Operations research, mathematical programming (90-XX)
2 Biology and other natural sciences (92-XX)
1 Harmonic analysis on Euclidean spaces (42-XX)
1 Numerical analysis (65-XX)
1 Mechanics of deformable solids (74-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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