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We provide a complete generators and relations presentation of the 2-dimensional extended unoriented and oriented bordism bicategories as symmetric monoidal bicategories.
Charles Ehresmann, Les prolongements d’une variété différentiable. I. Calcul des jets, prolongement principal , C. R. Acad. Sci. Paris 233
1951
Earlier work this paper cites.
by same author, Les prolongements d’une variété différentiable. II. L’espace des jets d’ordre r r de V n V_{n} dans V m V_{m} , C. R. Acad. Sci. Paris 233
1951
Earlier work this paper cites.
by same author, Les prolongements d’une variété différentiable. III. Transitivité des prolongements , C. R. Acad. Sci. Paris 233
1951
Earlier work this paper cites.
G. Th. Guilbaud and P. Rosenstiehl, Analyse algébrique d’un scrutin , Math. Sci. Humaines 4
1963
Earlier work this paper cites.
James Dillon Stasheff, Homotopy associativity of H H -spaces. I, II , Trans. Amer. Math. Soc. 108 (1963), 275-292; ibid. 108
1963
Earlier work this paper cites.
James R. Munkres, Elementary differential topology , Lectures given at Massachusetts Institute of Technology, Fall, vol. 1961, Princeton University Press, Princeton, N.J., 1966. MR MR0198479 (33 #6637)
1966
Earlier work this paper cites.
Jean Bénabou, Introduction to bicategories , Reports of the Midwest Category Seminar, Springer, Berlin, 1967, pp. 1–77. MR MR0220789 (36 #3841)
1967
Earlier work this paper cites.
Klaus Jänich, On the classification of O ( n ) O(n) -manifolds , Math. Ann. 176
1968
Earlier work this paper cites.
Jean Cerf, La stratification naturelle des espaces de fonctions différentiables réelles et le théorème de la pseudo-isotopie , Inst. Hautes Études Sci. Publ. Math. (1970), no. 39, 5–173. MR MR0292089 (45 #1176)
1970
Earlier work this paper cites.
Frank DeMeyer and Edward Ingraham, Separable algebras over commutative rings , Lecture Notes in Mathematics, Vol. 181, Springer-Verlag, Berlin, 1971. MR MR0280479 (43 #6199)
1971
Earlier work this paper cites.
Saunders MacLane, Categories for the working mathematician , Springer-Verlag, New York, 1971, Graduate Texts in Mathematics, Vol. 5. MR MR0354798 (50 #7275)
1971
Earlier work this paper cites.
I. R. Porteous, Simple singularities of maps , Proceedings of Liverpool Singularities Symposium, I (1969/70) (Berlin), Springer, 1971, pp. 286–307. Lecture Notes in Math., Vol. 192. MR MR0293646 (45 #2723)
1971
Earlier work this paper cites.
Ian R. Porteous, The second-order decomposition of Σ 2 \Sigma^{2} , Topology 11
1972
Earlier work this paper cites.
M. Golubitsky and V. Guillemin, Stable mappings and their singularities , Springer-Verlag, New York, 1973, Graduate Texts in Mathematics, Vol. 14. MR MR0341518 (49 #6269)
1973
Earlier work this paper cites.
John W. Gray, Formal category theory: adjointness for 2 2 -categories , Lecture Notes in Mathematics, Vol. 391, Springer-Verlag, Berlin-New York, 1974. MR 0371990 (51 #8207)
1974
Earlier work this paper cites.
G. M. Kelly and Ross Street, Review of the elements of 2 2 -categories , Category Seminar (Proc. Sem., Sydney, 1972/1973), Springer, Berlin, 1974, pp. 75–103. Lecture Notes in Math., Vol. 420. MR MR0357542 (50 #10010)
1974
Earlier work this paper cites.
Ross Street, Limits indexed by category-valued 2 2 -functors , J. Pure Appl. Algebra 8
1976
Earlier work this paper cites.
Peter W. Michor, Manifolds of differentiable mappings , Shiva Mathematics Series, vol. 3, Shiva Publishing Ltd., Nantwich, 1980. MR MR583436 (83g:58009)
1980
Earlier work this paper cites.
Michael Barr and Charles Wells, Toposes, triples and theories , Repr. Theory Appl. Categ. (2005), no. 12, x+288, Corrected reprint of the 1985 original [MR0771116]. MR 2178101
1985
Earlier work this paper cites.
André Joyal and Ross Street, Braided tensor categories , Macquarie Mathematics Report (1986), no. 860081
1986
Earlier work this paper cites.
Michael Atiyah, Topological quantum field theories , Inst. Hautes Études Sci. Publ. Math. (1988), no. 68, 175–186 (1989). MR MR1001453 (90e:57059)
1989
Earlier work this paper cites.
Albert Burroni, Higher-dimensional word problems with applications to equational logic , Theoret. Comput. Sci. 115
1991
Earlier work this paper cites.
by same author, Braided tensor categories , Adv. Math. 102
1993
Earlier work this paper cites.
Ivan Kolář, Peter W. Michor, and Jan Slovák, Natural operations in differential geometry , Springer-Verlag, Berlin, 1993. MR MR1202431 (94a:58004)
1993
Earlier work this paper cites.
G. M. Kelly and A. J. Power, Adjunctions whose counits are coequalizers, and presentations of finitary enriched monads , J. Pure Appl. Algebra 89
1993
Earlier work this paper cites.
Lawrence Breen, On the classification of 2 2 -gerbes and 2 2 -stacks , Astérisque (1994), no. 225, 160. MR 1301844 (95m:18006)
1994
Earlier work this paper cites.
M. Kapranov and V. Voevodsky, Braided monoidal 2 2 -categories and Manin-Schechtman higher braid groups , J. Pure Appl. Algebra 92
1994
Earlier work this paper cites.
M. M. Kapranov and V. A. Voevodsky, 2 2 -categories and Zamolodchikov tetrahedra equations , Algebraic groups and their generalizations: quantum and infinite-dimensional methods (University Park, PA, 1991), Proc. Sympos. Pure Math., vol. 56, Amer. Math. Soc., Providence, RI, 1994, pp. 177–259. MR MR1278735 (95f:18011)
1994
Cited alongside, same era.
1994
Cited alongside, same era.
John C. Baez and James Dolan, Higher-dimensional algebra and topological quantum field theory , J. Math. Phys. 36
1995
Cited alongside, same era.
R. Gordon, A. J. Power, and Ross Street, Coherence for tricategories , Mem. Amer. Math. Soc. 117
1995
Cited alongside, same era.
by same author, Higher operads, higher categories , London Mathematical Society Lecture Note Series, vol. 298, Cambridge University Press, Cambridge, 2004. MR MR2094071 (2005h:18030)
2004
Later among the works it cites.
Graeme Segal, The definition of conformal field theory , Topology, geometry and quantum field theory, London Math. Soc. Lecture Note Ser., vol. 308, Cambridge Univ. Press, Cambridge, 2004, pp. 421–577. MR MR2079383 (2005h:81334)
2004
Later among the works it cites.
Stephan Stolz and Peter Teichner, What is an elliptic object? , Topology, geometry and quantum field theory, London Math. Soc. Lecture Note Ser., vol. 308, Cambridge Univ. Press, Cambridge, 2004, pp. 247–343. MR MR2079378 (2005m:58048)
2004
Later among the works it cites.
Michael H. Freedman, Alexei Kitaev, Chetan Nayak, Johannes K. Slingerland, Kevin Walker, and Zhenghan Wang, Universal manifold pairings and positivity , Geom. Topol. 9
2005
Later among the works it cites.
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Frank Quinn, Lectures on axiomatic topological quantum field theory , Geometry and quantum field theory (Park City, UT, 1991), IAS/Park City Math. Ser., vol. 1, Amer. Math. Soc., Providence, RI, 1995, pp. 323–453. MR MR1338394 (96e:57021)
1995
Cited alongside, same era.
Stephen Sawin, Direct sum decompositions and indecomposable TQFTs , J. Math. Phys. 36
1995
Cited alongside, same era.
Lowell Abrams, Two-dimensional topological quantum field theories and Frobenius algebras , J. Knot Theory Ramifications 5
1996
Cited alongside, same era.
1996
Cited alongside, same era.
Boris Dubrovin, Geometry of 2 2 D topological field theories , Integrable systems and quantum groups (Montecatini Terme, 1993), Lecture Notes in Math., vol. 1620, Springer, Berlin, 1996, pp. 120–348. MR MR1397274 (97d:58038)
1996
Cited alongside, same era.
J. Scott Carter, Joachim H. Rieger, and Masahico Saito, A combinatorial description of knotted surfaces and their isotopies , Adv. Math. 127
1997
Cited alongside, same era.
Brian Day and Ross Street, Monoidal bicategories and Hopf algebroids , Adv. Math. 129
1997
Cited alongside, same era.
M. A. Batanin, Computads for finitary monads on globular sets , Higher category theory (Evanston, IL, 1997), Contemp. Math., vol. 230, Amer. Math. Soc., Providence, RI, 1998, pp. 37–57. MR 1664991 (99i:18011)
1998
Cited alongside, same era.
M. J. Hopkins and I. M. Singer, Quadratic functions in geometry, topology, and M-theory , J. Differential Geom. 70
2005
Later among the works it cites.
Angelo Vistoli, Grothendieck topologies, fibered categories and descent theory , Fundamental algebraic geometry, Math. Surveys Monogr., vol. 123, Amer. Math. Soc., Providence, RI, 2005, pp. 1–104. MR MR2223406
2005
Later among the works it cites.
Michael Nicholas Gurski, An algebraic theory of tricategories , ProQuest LLC, Ann Arbor, MI, 2006, Thesis (Ph.D.)–The University of Chicago. MR 2717302
2006
Later among the works it cites.
Eugenia Cheng and Nick Gurski, The periodic table of n n -categories for low dimensions. I. Degenerate categories and degenerate bicategories , Categories in algebra, geometry and mathematical physics, Contemp. Math., vol. 431, Amer. Math. Soc., Providence, RI, 2007, pp. 143–164. MR 2342826 (2008h:18004)
2007
Later among the works it cites.
by same author, The Eckmann-Hilton argument and higher operads , Adv. Math. 217
2008
Later among the works it cites.
Matthias Kreck and Peter Teichner, Positive topological field theories and manifolds of dimension ¿ 4 , Preprint . To appear in Journal of Topology, Volume 1 (2008), 663–670,
2008
Later among the works it cites.
David Ayala, Geometric cobordism categories , ProQuest LLC, Ann Arbor, MI, 2009, Thesis (Ph.D.)–Stanford University. MR 2713365
2009
Later among the works it cites.
Jacob Lurie, On the classification of topological field theories , Current developments in mathematics, 2008, Int. Press, Somerville, MA, 2009, pp. 129–280. MR 2555928 (2010k:57064)
2009
Later among the works it cites.
by same author, Icons , Applied Categorical Structures 18
2010
Later among the works it cites.
by same author, The periodic table of n n -categories II: Degenerate tricategories , Cah. Topol. Géom. Différ. Catég. 52
2011
Closest in time.
Nick Gurski, Loop spaces, and coherence for monoidal and braided monoidal bicategories , Adv. Math. 226
2011
Closest in time.
Jiří Adámek, Stefan Milius, and Lawrence S. Moss, On finitary functors and their presentations , Coalgebraic methods in computer science, Lecture Notes in Comput. Sci., vol. 7399, Springer, Heidelberg, 2012, pp. 51–70. MR 3003200
2012
Closest in time.
by same author, Biequivalences in tricategories , Theory Appl. Categ. 26
2012
Closest in time.
Niles Johnson and Angélica M. Osorno, Modeling stable one-types , Theory Appl. Categ. 26
2012
Closest in time.
Carlos Simpson, Homotopy theory of higher categories , New Mathematical Monographs, vol. 19, Cambridge University Press, Cambridge, 2012. MR 2883823 (2012m:18019)
2012
Closest in time.
Louis Funar, Torus bundles not distinguished by TQFT invariants , Geom. Topol. 17
2013
Closest in time.
Nick Gurski and Angélica M. Osorno, Infinite loop spaces, and coherence for symmetric monoidal bicategories , Adv. Math. 246
2013
Closest in time.
by same author, Coherence in three-dimensional category theory , Cambridge Tracts in Mathematics, vol. 201, Cambridge University Press, Cambridge, 2013. MR 3076451
2013
Closest in time.
Bruce Bartlett, Quasistrict symmetric monoidal 2-categories via wire diagrams , Preprint, 2014
2014
Closest in time.
by same author, Extended 3-dimensional bordism as the theory of modular objects , Preprint, 2014
2014
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by same author, Modular categories are representations of modular objects , Preprint, 2014
2014
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Nick Gurski, Niles Johnson, and Angélica M. Osorno, Msri notes , May 2014
2014
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André Henriques, Three-tier cfts from frobenius algebras , Topology and Field Theories, Contemporary Mathematics, vol. 613, American Mathematical Society, Providence, RI, 2014
2014
Closest in time.