Volume 19, issue 2 (2019)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 25
Issue 6, 3145–3787
Issue 5, 2527–3144
Issue 4, 1917–2526
Issue 3, 1265–1915
Issue 2, 645–1264
Issue 1, 1–644

Volume 24, 9 issues

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
 
Author index
To appear
 
Other MSP journals
A note on the $(\infty,n)$–category of cobordisms

Damien Calaque and Claudia Scheimbauer

Algebraic & Geometric Topology 19 (2019) 533–655
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)