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Tori detect invertibility of topological field theories

Christopher J Schommer-Pries

Geometry & Topology 22 (2018) 2713–2756
1 M Atiyah, Topological quantum field theories, Inst. Hautes Études Sci. Publ. Math. 68 (1988) 175 MR1001453
2 J C Baez, J Dolan, Higher-dimensional algebra and topological quantum field theory, J. Math. Phys. 36 (1995) 6073 MR1355899
3 B Bartlett, C Douglas, C Schommer-Pries, J Vicary, Modular categories as representations of the 3–dimensional bordism 2–category, preprint (2015) arXiv:1509.06811
4 C Barwick, C J Schommer-Pries, On the unicity of the homotopy theory of higher categories, preprint (2011) arXiv:1112.0040
5 J Bénabou, Introduction to bicategories, from: "Reports of the Midwest Category Seminar" (editors A Dold, B Eckmann), Springer (1967) 1 MR0220789
6 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
7 D Calaque, C Scheimbauer, A note on the (,n)–category of cobordisms, preprint (2015) arXiv:1112.0040
8 L Crane, L H Kauffman, D Yetter, Evaluating the Crane–Yetter invariant, from: "Quantum topology" (editors L H Kauffman, R A Baadhio), Ser. Knots Everything 3, World Scientific (1993) 131 MR1273570
9 L Crane, L H Kauffman, D N Yetter, State-sum invariants of 4–manifolds, J. Knot Theory Ramifications 6 (1997) 177 MR1452438
10 L Crane, D Yetter, A categorical construction of 4D topological quantum field theories, from: "Quantum topology" (editors L H Kauffman, R A Baadhio), Ser. Knots Everything 3, World Scientific (1993) 120 MR1273569
11 C L Douglas, C J Schommer-Pries, N Snyder, Dualizable tensor categories, preprint (2013) arXiv:1312.7188
12 M Feshbach, A A Voronov, A higher category of cobordisms and topological quantum field theory, preprint (2011) arXiv:1108.3349
13 D S Freed, Higher algebraic structures and quantization, Comm. Math. Phys. 159 (1994) 343 MR1256993
14 D S Freed, 4-3-2-8-7-6, talk slides (2012)
15 D S Freed, Anomalies and invertible field theories, from: "String-Math 2013" (editors R Donagi, M R Douglas, L Kamenova, M Roček), Proc. Sympos. Pure Math. 88, Amer. Math. Soc. (2014) 25 MR3330283
16 D S Freed, Short-range entanglement and invertible field theories, preprint (2014) arXiv:1406.7278
17 D S Freed, M J Hopkins, J Lurie, C Teleman, Topological quantum field theories from compact Lie groups, from: "A celebration of the mathematical legacy of Raoul Bott" (editor P R Kotiuga), CRM Proc. Lecture Notes 50, Amer. Math. Soc. (2010) 367 MR2648901
18 D S Freed, C Teleman, Relative quantum field theory, Comm. Math. Phys. 326 (2014) 459 MR3165462
19 S Galatius, U Tillmann, I Madsen, M Weiss, The homotopy type of the cobordism category, Acta Math. 202 (2009) 195 MR2506750
20 S Gunningham, Spin Hurwitz numbers and topological quantum field theory, Geom. Topol. 20 (2016) 1859 MR3548460
21 C M Jian, Examples of (n+1)–D TQFT with 1–dimensional Hilbert spaces on n–torus and n–sphere but higher-dimensional Hilbert spaces on other n–manifolds, MathOverflow (2015)
22 A Kapustin, Topological field theory, higher categories, and their applications, from: "Proceedings of the International Congress of Mathematicians, III" (editors R Bhatia, A Pal, G Rangarajan, V Srinivas, M Vanninathan), Hindustan Book Agency (2010) 2021 MR2827874
23 A Kapustin, A Turzillo, Equivariant topological quantum field theory and symmetry protected topological phases, J. High Energy Phys. (2017) MR3657691
24 T Kerler, V V Lyubashenko, Non-semisimple topological quantum field theories for 3–manifolds with corners, 1765, Springer (2001) MR1862634
25 R J Lawrence, Triangulations, categories and extended topological field theories, from: "Quantum topology" (editors L H Kauffman, R A Baadhio), Ser. Knots Everything 3, World Scientific (1993) 191 MR1273575
26 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
27 M Müger, Galois theory for braided tensor categories and the modular closure, Adv. Math. 150 (2000) 151 MR1749250
28 H Nguyen, Higher bordism categories, Master’s thesis, Universität Bonn (2014)
29 P Pstrągowski, On dualizable objects in monoidal bicategories, framed surfaces and the cobordism hypothesis, preprint (2014) arXiv:1411.6691
30 O Randal-Williams, Embedded cobordism categories and spaces of submanifolds, Int. Math. Res. Not. 2011 (2011) 572 MR2764873
31 J Roberts, Skein theory and Turaev–Viro invariants, Topology 34 (1995) 771 MR1362787
32 C Scheimbauer, Factorization homology as a fully extended topological field theory, Doctoral thesis, ETH Zürich (2014)
33 C J Schommer-Pries, The classification of two-dimensional extended topological field theories, PhD thesis, University of California, Berkeley (2009) MR2713992
34 C Schommer-Pries, Invertible topological field theories, preprint (2017) arXiv:1712.08029
35 G Segal, The definition of conformal field theory, from: "Topology, geometry and quantum field theory" (editor U Tillmann), London Math. Soc. Lecture Note Ser. 308, Cambridge Univ. Press (2004) 421 MR2079383
36 G Segal, Locality of holomorphic bundles, and locality in quantum field theory, from: "The many facets of geometry" (editors O García-Prada, J P Bourguignon, S Salamon), Oxford Univ. Press (2010) 164 MR2681691
37 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
38 Y Tsumura, A 2–categorical extension of the Reshetikhin–Turaev theory, J. Pure Appl. Algebra 219 (2015) 4953 MR3351570
39 K Walker, Topological quantum field theories, preprint (2006)
40 K Walker, Premodular TQFTs, talk slides (2014)
41 K Walker, Z Wang, (3+1)–TQFTs and topological insulators, preprint (2011) arXiv:1104.2632