Algebraic & Geometric Topology Volume 19, issue 2 (2019)

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A note on the $(\infty,n)$–category of cobordisms

Damien Calaque and Claudia Scheimbauer

Algebraic & Geometric Topology 19 (2019) 533–655

DOI: 10.2140/agt.2019.19.533

Bibliography

1	L Abrams, Two-dimensional topological quantum field theories and Frobenius algebras, J. Knot Theory Ramifications 5 (1996) 569 MR1414088
2	J C Baez, J Dolan, Higher-dimensional algebra and topological quantum field theory, J. Math. Phys. 36 (1995) 6073 MR1355899
3	C Barwick, (∞,n)–Cat as a closed model category, PhD thesis, University of Pennsylvania (2005) MR2706984
4	C Barwick, D M Kan, Partial model categories and their simplicial nerves, preprint (2011) arXiv:1102.2512
5	C Barwick, D M Kan, Relative categories: another model for the homotopy theory of homotopy theories, Indag. Math. 23 (2012) 42 MR2877401
6	C Barwick, C Schommer-Pries, On the unicity of the homotopy theory of higher categories, preprint (2011) arXiv:1112.0040
7	J E Bergner, Three models for the homotopy theory of homotopy theories, Topology 46 (2007) 397 MR2321038
8	J E Bergner, A survey of (∞,1)–categories, from: "Towards higher categories" (editors J C Baez, J P May), IMA Vol. Math. Appl. 152, Springer (2010) 69 MR2664620
9	J E Bergner, Models for (∞,n)–categories and the cobordism hypothesis, from: "Mathematical foundations of quantum field theory and perturbative string theory" (editors H Sati, U Schreiber), Proc. Sympos. Pure Math. 83, Amer. Math. Soc. (2011) 17 MR2742424
10	J E Bergner, C Rezk, Comparison of models for (∞,n)–categories, I, Geom. Topol. 17 (2013) 2163 MR3109865
11	J E Bergner, C Rezk, Comparison of models for (∞,n)–categories, II, preprint (2014) arXiv:1406.4182
12	M Bökstedt, I Madsen, The cobordism category and Waldhausen’s K–theory, from: "An alpine expedition through algebraic topology" (editors C Ausoni, K Hess, B Johnson, W Lück, J Scherer), Contemp. Math. 617, Amer. Math. Soc. (2014) 39 MR3243393
13	D Calaque, C Scheimbauer, Factorization homology as a fully extended topological field theory, in preparation
14	J A Campbell, Derived Koszul duality and topological Hochschild homology, preprint (2014) arXiv:1401.5147
15	G Caviglia, G Horel, Rigidification of higher categorical structures, Algebr. Geom. Topol. 16 (2016) 3533 MR3584266
16	W G Dwyer, D M Kan, Function complexes in homotopical algebra, Topology 19 (1980) 427 MR584566
17	W G Dwyer, D M Kan, J H Smith, Homotopy commutative diagrams and their realizations, J. Pure Appl. Algebra 57 (1989) 5 MR984042
18	C Ehresmann, Catégories structurées, Ann. Sci. École Norm. Sup. 80 (1963) 349 MR0197529
19	S Galatius, Stable homology of automorphism groups of free groups, Ann. of Math. 173 (2011) 705 MR2784914
20	S Galatius, O Randal-Williams, Monoids of moduli spaces of manifolds, Geom. Topol. 14 (2010) 1243 MR2653727
21	S Galatius, U Tillmann, I Madsen, M Weiss, The homotopy type of the cobordism category, Acta Math. 202 (2009) 195 MR2506750
22	D Gay, K Wehrheim, C Woodward, Connected cerf theory, (2012)
23	D Gepner, R Haugseng, Enriched ∞–categories via non-symmetric ∞–operads, Adv. Math. 279 (2015) 575 MR3345192
24	A Grothendieck, Pursuing stacks, unpublished manuscript (1983)
25	R Haugseng, Iterated spans and classical topological field theories, Math. Z. 289 (2018) 1427 MR3830256
26	P S Hirschhorn, Model categories and their localizations, 99, Amer. Math. Soc. (2003) MR1944041
27	A Hirschowitz, C Simpson, Descente pour les n–champs, preprint (1998) arXiv:math/9807049
28	G Horel, A model structure on internal categories in simplicial sets, Theory Appl. Categ. 30 (2015) 704 MR3356341
29	T Johnson-Freyd, C Scheimbauer, (Op)lax natural transformations, twisted quantum field theories, and “even higher” Morita categories, Adv. Math. 307 (2017) 147 MR3590516
30	A Joyal, Disks, duality, and Theta-categories, preprint (1997)
31	A Joyal, Notes on quasicategories, unpublished manuscript (2008)
32	J Kock, Frobenius algebras and 2D topological quantum field theories, 59, Cambridge Univ. Press (2004) MR2037238
33	A D Lauda, H Pfeiffer, Open-closed strings : two-dimensional extended TQFTs and Frobenius algebras, Topology Appl. 155 (2008) 623 MR2395583
34	G Laures, On cobordism of manifolds with corners, Trans. Amer. Math. Soc. 352 (2000) 5667 MR1781277
35	J M Lee, Introduction to smooth manifolds, 218, Springer (2013) MR2954043
36	Z L Low, Cocycles in categories of fibrant objects, preprint (2015) arXiv:1502.03925
37	Z L Low, A Mazel-Gee, From fractions to complete Segal spaces, Homology Homotopy Appl. 17 (2015) 321 MR3350085
38	J Lurie, Higher topos theory, 170, Princeton Univ. Press (2009) MR2522659
39	J Lurie, (∞,2)–Categories and the Goodwillie calculus, I, preprint (2009) arXiv:0905.0462
40	J Lurie, On the classification of topological field theories, from: "Current developments in mathematics, 2008" (editors D Jerison, B Mazur, T Mrowka, W Schmid, R Stanley, S T Yau), Int. (2009) 129 MR2555928
41	J Lurie, Higher algebra, book project (2017)
42	S Mac Lane, Natural associativity and commutativity, Rice Univ. Studies 49 (1963) 28 MR0170925
43	J Milnor, Morse theory, 51, Princeton Univ. Press (1963) MR0163331
44	C Rezk, Fibrations and homotopy colimits of simplicial sheaves, preprint (1998) arXiv:math/9811038
45	C Rezk, A model for the homotopy theory of homotopy theory, Trans. Amer. Math. Soc. 353 (2001) 973 MR1804411
46	C Rezk, A Cartesian presentation of weak n–categories, Geom. Topol. 14 (2010) 521 MR2578310
47	E Riehl, Category theory in context, Dover (2016)
48	C Scheimbauer, Factorization homology as a fully extended topological field theory, PhD thesis, ETH Zürich (2014)
49	C J Schommer-Pries, The classification of two-dimensional extended topological field theories, PhD thesis, University of California, Berkeley (2009) MR2713992
50	G Segal, Categories and cohomology theories, Topology 13 (1974) 293 MR0353298
51	C Simpson, On the Breen–Baez–Dolan stabilization hypothesis for Tamsamani’s weak n–categories, preprint (1998) arXiv:math/9810058
52	B Toen, Dualité de tannaka supérieure, I : Structures monoidales, preprint (2000)
53	B Toën, Vers une axiomatisation de la théorie des catégories supérieures, K–Theory 34 (2005) 233 MR2182378
54	B Toen, G Vezzosi, Segal topoi and stacks over Segal categories, preprint (2002) arXiv:math/0212330
55	B Toën, G Vezzosi, Homotopical algebraic geometry, I : Topos theory, Adv. Math. 193 (2005) 257 MR2137288
56	B Toën, G Vezzosi, Caractères de Chern, traces équivariantes et géométrie algébrique dérivée, Selecta Math. 21 (2015) 449 MR3338682
57	Y Zhao, Extended topological field theories and the cobordism hypothesis, Master’s thesis, Université Paris XI (Paris-Sud) and Università degli studi di Padova (2013)