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

Volume 26
Issue 5, 1597–1963
Issue 4, 1229–1596
Issue 3, 825–1227
Issue 2, 411–824
Issue 1, 1–410

Volume 25, 9 issues

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
Smooth one-dimensional topological field theories are vector bundles with connection

Daniel Berwick-Evans and Dmitri Pavlov

Algebraic & Geometric Topology 23 (2023) 3707–3743
Bibliography
1 J C Baez, J Dolan, Higher-dimensional algebra and topological quantum field theory, J. Math. Phys. 36 (1995) 6073 MR1355899
2 C Barwick, On left and right model categories and left and right Bousfield localizations, Homology Homotopy Appl. 12 (2010) 245 MR2771591
3 M Benini, M Perin, A Schenkel, Smooth 1–dimensional algebraic quantum field theories, Ann. Henri Poincaré 23 (2022) 2069 MR4420570
4 C Berger, I Moerdijk, On an extension of the notion of Reedy category, Math. Z. 269 (2011) 977 MR2860274
5 J E Bergner, C Rezk, Reedy categories and the Θ–construction, Math. Z. 274 (2013) 499 MR3054341
6 A K Bousfield, E M Friedlander, Homotopy theory of Γ–spaces, spectra, and bisimplicial sets, from: "Geometric applications of homotopy theory, II" (editors M G Barratt, M E Mahowald), Lecture Notes in Math. 658, Springer (1978) 80 MR513569
7 U Bunke, P Turner, S Willerton, Gerbes and homotopy quantum field theories, Algebr. Geom. Topol. 4 (2004) 407 MR2077672
8 A Caetano, R F Picken, An axiomatic definition of holonomy, Internat. J. Math. 5 (1994) 835 MR1298997
9 D Calaque, C Scheimbauer, A note on the (,n)–category of cobordisms, Algebr. Geom. Topol. 19 (2019) 533 MR3924174
10 D Dugger, S Hollander, D C Isaksen, Hypercovers and simplicial presheaves, Math. Proc. Cambridge Philos. Soc. 136 (2004) 9 MR2034012
11 D S Freed, Classical Chern–Simons theory, I, Adv. Math. 113 (1995) 237 MR1337109
12 S Galatius, I Madsen, U Tillmann, M Weiss, The homotopy type of the cobordism category, Acta Math. 202 (2009) 195 MR2506750
13 D Grady, D Pavlov, Extended field theories are local and have classifying spaces, preprint (2020) arXiv:2011.01208v2
14 D Grady, D Pavlov, The geometric cobordism hypothesis, preprint (2021) arXiv:2111.01095v1
15 P S Hirschhorn, Model categories and their localizations, 99, Amer. Math. Soc. (2003) MR1944041
16 J F Jardine, Simplicial presheaves, J. Pure Appl. Algebra 47 (1987) 35 MR906403
17 S Kobayashi, La connexion des variétés fibrées, II, C. R. Acad. Sci. Paris 238 (1954) 443 MR60889
18 M Ludewig, A Stoffel, A framework for geometric field theories and their classification in dimension one, Symmetry Integrability Geom. Methods Appl. 17 (2021) 072 MR4289685
19 J Lurie, Higher topos theory, 170, Princeton Univ. Press (2009) MR2522659
20 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), International (2009) 129 MR2555928
21 C Rezk, A model for the homotopy theory of homotopy theory, Trans. Amer. Math. Soc. 353 (2001) 973 MR1804411
22 U Schreiber, K Waldorf, Parallel transport and functors, J. Homotopy Relat. Struct. 4 (2009) 187 MR2520993
23 G Segal, Categories and cohomology theories, Topology 13 (1974) 293 MR353298
24 G Segal, Elliptic cohomology (after Landweber–Stong, Ochanine, Witten, and others), from: "Séminaire Bourbaki, 1987/88", Astérisque 161–162, Soc. Mat. France (1988) 187 MR992209
25 S Stolz, P Teichner, What is an elliptic object?, from: "Topology, geometry and quantum field theory" (editor U Tillman), London Math. Soc. Lecture Note Ser. 308, Cambridge Univ. Press (2004) 247 MR2079378
26 S Stolz, P Teichner, Supersymmetric field theories and generalized cohomology, 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) 279 MR2742432