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## Kirby, Robion Cromwell

Compute Distance To:
 Author ID: kirby.robion-c 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
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#### Co-Authors

 19 single-authored 9 Melvin, Paul M. 7 Gay, David T. 4 Akbulut, Selman 4 Siebenmann, Laurence C. 3 Scharlemann, Martin G. 3 Taylor, Laurence Robert 2 Thompson, Abigail A. 1 Abrams, Aaron 1 Edwards, Robert Duncan 1 Freedman, Michael Hartley 1 Gordon, Cameron McA. 1 Harer, John L. 1 Kas, Arnold 1 Krushkal, Vyacheslav S. 1 Lickorish, William Bernard Raymond 1 Teichner, Peter 1 Wang, Zhenghan 1 Zhang, Xingru
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#### Serials

 5 Geometry & Topology 4 Proceedings of the National Academy of Sciences of the United States of America 3 Inventiones Mathematicae 3 Topology 3 Notices of the American Mathematical Society 3 Annals of Mathematics. Second Series 3 Bulletin of the American Mathematical Society 2 Mathematische Annalen 2 Turkish Journal of Mathematics 1 Communications in Mathematical Physics 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Uspekhi Matematicheskikh Nauk [N. S.] 1 Commentarii Mathematici Helvetici 1 Memoirs of the American Mathematical Society 1 Michigan Mathematical Journal 1 Proceedings of the American Mathematical Society 1 New Zealand Journal of Mathematics 1 Annals of Mathematics Studies 1 Contemporary Mathematics 1 Lecture Notes in Mathematics 1 Geometry and Topology Monographs
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#### Fields

 47 Manifolds and cell complexes (57-XX) 5 General and overarching topics; collections (00-XX) 5 Algebraic topology (55-XX) 4 Quantum theory (81-XX) 2 Algebraic geometry (14-XX) 2 Group theory and generalizations (20-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Differential geometry (53-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Computer science (68-XX) 1 History and biography (01-XX) 1 Number theory (11-XX) 1 Nonassociative rings and algebras (17-XX) 1 Category theory; homological algebra (18-XX) 1 Statistical mechanics, structure of matter (82-XX)

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

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