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

Volume 30
Issue 3, 835–1201
Issue 2, 389–833
Issue 1, 1–388

Volume 29, 9 issues

Volume 28, 9 issues

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
 
Author index
To appear
 
Other MSP journals
Unit inclusion in a (nonsemisimple) braided tensor category and (noncompact) relative TQFTs

Benjamin Haïoun

Geometry & Topology 29 (2025) 2175–2216
Bibliography
1 J Adámek, J Rosický, Locally presentable and accessible categories, 189, Cambridge Univ. Press (1994) MR1294136
2 D Ayala, J Francis, The cobordism hypothesis, preprint (2017) arXiv:1705.02240
3 J C Baez, J Dolan, Higher-dimensional algebra and topological quantum field theory, J. Math. Phys. 36 (1995) 6073 MR1355899
4 B Bartlett, C L Douglas, C J Schommer-Pries, J Vicary, Modular categories as representations of the 3-dimensional bordism 2-category, preprint (2015) arXiv:1509.06811
5 C Blanchet, F Costantino, N Geer, B Patureau-Mirand, Nonsemisimple TQFTs, Reidemeister torsion and Kashaev’s invariants, Adv. Math. 301 (2016) 1 MR3539369
6 M Brandenburg, A Chirvasitu, T Johnson-Freyd, Reflexivity and dualizability in categorified linear algebra, Theory Appl. Categ. 30 (2015) 23 MR3361309
7 A Brochier, D Jordan, P Safronov, N Snyder, Invertible braided tensor categories, Algebr. Geom. Topol. 21 (2021) 2107 MR4302495
8 A Brochier, D Jordan, N Snyder, On dualizability of braided tensor categories, Compos. Math. 157 (2021) 435 MR4228258
9 F Costantino, N Geer, B Haïoun, B Patureau-Mirand, Skein (3+1)-TQFTs from non-semisimple ribbon categories, preprint (2023) arXiv:2306.03225
10 M De Renzi, Construction of extended topological quantum field theories, PhD thesis, Université Sorbonne Paris Cité (2017)
11 M De Renzi, Extended TQFTs from non-semisimple modular categories, Indiana Univ. Math. J. 70 (2021) 1769 MR4340481
12 M De Renzi, A M Gainutdinov, N Geer, B Patureau-Mirand, I Runkel, 3-dimensional TQFTs from non-semisimple modular categories, Selecta Math. 28 (2022) 42 MR4370375
13 C L Douglas, C Schommer-Pries, N Snyder, Dualizable tensor categories, 1308, Amer. Math. Soc. (2020) MR4254952
14 P Etingof, S Gelaki, D Nikshych, V Ostrik, Tensor categories, 205, Amer. Math. Soc. (2015) MR3242743
15 D S Freed, Remarks on fully extended 3-dimensional topological field theories, lecture slides (2011)
16 D S Freed, C Teleman, Relative quantum field theory, Comm. Math. Phys. 326 (2014) 459 MR3165462
17 D S Freed, C Teleman, Gapped boundary theories in three dimensions, Comm. Math. Phys. 388 (2021) 845 MR4334249
18 N Geer, J Kujawa, B Patureau-Mirand, M-traces in (non-unimodular) pivotal categories, Algebr. Represent. Theory 25 (2022) 759 MR4421818
19 R Gelca, Topological quantum field theory with corners based on the Kauffman bracket, Comment. Math. Helv. 72 (1997) 216 MR1470089
20 D Grady, D Pavlov, The geometric cobordism hypothesis, preprint (2021) arXiv:2111.01095
21 O Gwilliam, C Scheimbauer, Duals and adjoints in higher Morita categories, preprint (2018) arXiv:1804.10924
22 R Haugseng, The higher Morita category of 𝔼n-algebras, Geom. Topol. 21 (2017) 1631 MR3650080
23 T Johnson-Freyd, Heisenberg-picture quantum field theory, from: "Representation theory, mathematical physics, and integrable systems", Progr. Math. 340, Birkhäuser (2021) 371 MR4391354
24 T Johnson-Freyd, C Scheimbauer, (Op)lax natural transformations, twisted quantum field theories, and “even higher” Morita categories, Adv. Math. 307 (2017) 147 MR3590516
25 J Lurie, On the classification of topological field theories, from: "Current developments in mathematics, 2008", International (2009) 129 MR2555928
26 J Lurie, Higher algebra, book project (2017)
27 E Riehl, D Verity, Homotopy coherent adjunctions and the formal theory of monads, Adv. Math. 286 (2016) 802 MR3415698
28 C Scheimbauer, Factorization homology as a fully extended topological field theory, PhD thesis, ETH Zürich (2014)
29 C J Schommer-Pries, Dualizability in low-dimensional higher category theory, from: "Topology and field theories", Contemp. Math. 613, Amer. Math. Soc. (2014) 111 MR3221292
30 S Stolz, P Teichner, Supersymmetric field theories and generalized cohomology, from: "Mathematical foundations of quantum field theory and perturbative string theory", Proc. Sympos. Pure Math. 83, Amer. Math. Soc. (2011) 279 MR2742432
31 V G Turaev, Quantum invariants of knots and 3–manifolds, 18, de Gruyter (1994) MR1292673
32 K Walker, On Witten’s 3-manifold invariants, unpublished notes (1991)
33 K Walker, TQFTs, incomplete notes (2006)
34 E Witten, Quantum field theory and the Jones polynomial, Comm. Math. Phys. 121 (1989) 351 MR990772