Algebraic & Geometric Topology Volume 22, issue 4 (2022)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Twisted loop transgression and higher Jandl gerbes over finite groupoids

Behrang Noohi and Matthew B Young

Algebraic & Geometric Topology 22 (2022) 1663–1712

DOI: 10.2140/agt.2022.22.1663

Bibliography

1	M F Atiyah, K–theory and reality, Q. J. Math. 17 (1966) 367 MR206940
2	M F Atiyah, G B Segal, Equivariant K–theory and completion, J. Differential Geom. 3 (1969) 1 MR259946
3	P Bantay, Symmetric products, permutation orbifolds and discrete torsion, Lett. Math. Phys. 63 (2003) 209 MR1992886
4	M Barkeshli, P Bonderson, M Cheng, C M Jian, K Walker, Reflection and time reversal symmetry enriched topological phases of matter: path integrals, non-orientable manifolds, and anomalies, Comm. Math. Phys. 374 (2020) 1021 MR4072236
5	E Bernaschini, C Galindo, M Mombelli, Group actions on 2–categories, Manuscripta Math. 159 (2019) 81 MR3936135
6	V Braun, Orientifolds and K–theory, from: "Progress in string, field and particle theory" (editors L Baulieu, E Rabinovici, J Harvey, B Pioline, P Windey), NATO Sci. Ser. II 104, Springer (2003) 369
7	T Bröcker, T tom Dieck, Representations of compact Lie groups, 98, Springer (1985) MR781344
8	J L Brylinski, Loop spaces, characteristic classes and geometric quantization, 107, Birkhäuser (1993) MR1197353
9	J L Brylinski, D A McLaughlin, The geometry of degree-four characteristic classes and of line bundles on loop spaces, I, Duke Math. J. 75 (1994) 603 MR1291698
10	S Bunk, R J Szabo, Fluxes, bundle gerbes and 2–Hilbert spaces, Lett. Math. Phys. 107 (2017) 1877 MR3690037
11	E Diaconescu, G Moore, D S Freed, The M-theory 3–form and E₈ gauge theory, from: "Elliptic cohomology" (editors H R Miller, D C Ravenel), Lond. Math. Soc. Lect. Note Ser. 342, Cambridge Univ. Press (2007) 44 MR2330507
12	R Dijkgraaf, V Pasquier, P Roche, Quasi Hopf algebras, group cohomology and orbifold models, Nuclear Part. Phys. Proc. 18B (1990) 60 MR1128130
13	J Distler, D S Freed, G W Moore, Orientifold précis, 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) 159 MR2742428
14	J Distler, D S Freed, G W Moore, Spin structures and superstrings, from: "Surveys in differential geometry, XV : Perspectives in mathematics and physics" (editors T Mrowka, S T Yau), Surv. Differ. Geom. 15, International (2011) 99 MR2815726
15	M Douglas, D-branes and discrete torsion, preprint (1998) arXiv:hep-th/9807235
16	P Etingof, S Gelaki, D Nikshych, V Ostrik, Tensor categories, 205, Amer. Math. Soc. (2015) MR3242743
17	C K Fok, The real K–theory of compact Lie groups, Symmetry Integrability Geom. Methods Appl. 10 (2014) MR3210613
18	C K Fok, Equivariant twisted real K–theory of compact Lie groups, J. Geom. Phys. 124 (2018) 325 MR3754518
19	D S Freed, Higher algebraic structures and quantization, Comm. Math. Phys. 159 (1994) 343 MR1256993
20	D S Freed, M J Hopkins, C Teleman, Loop groups and twisted K–theory, I, J. Topol. 4 (2011) 737 MR2860342
21	D S Freed, G W Moore, Twisted equivariant matter, Ann. Henri Poincaré 14 (2013) 1927 MR3119923
22	J Fuchs, C Schweigert, A Valentino, A geometric approach to boundaries and surface defects in Dijkgraaf–Witten theories, Comm. Math. Phys. 332 (2014) 981 MR3262619
23	K Gawędzki, R R Suszek, K Waldorf, Bundle gerbes for orientifold sigma models, Adv. Theor. Math. Phys. 15 (2011) 621 MR2929686
24	K Gomi, Y Terashima, Discrete torsion phases as topological actions, Comm. Math. Phys. 287 (2009) 889 MR2486666
25	M J Hopkins, N J Kuhn, D C Ravenel, Generalized group characters and complex oriented cohomology theories, J. Amer. Math. Soc. 13 (2000) 553 MR1758754
26	A Kapustin, A Turzillo, Equivariant topological quantum field theory and symmetry protected topological phases, J. High Energy Phys. 2017 (2017) MR3657691
27	M Karoubi, Sur la K–théorie équivariante, from: "Séminaire Heidelberg–Saarbrücken–Strasbourg sur la K–théorie" (editors A Dold, B Eckmann), Lecture Notes in Math. 136, Springer (1970) 187 MR0268253
28	G Karpilovsky, Projective representations of finite groups, 94, Dekker (1985) MR788161
29	M Kim, Arithmetic Chern–Simons theory, I, from: "Galois covers, Grothendieck–Teichmüller theory and dessins d’enfants" (editors F Neumann, S Schroll), Springer Proc. Math. Stat. 330, Springer (2020) 155 MR4166930
30	L Kong, Y Tian, S Zhou, The center of monoidal 2–categories in 3 + 1D Dijkgraaf–Witten theory, Adv. Math. 360 (2020) MR4037491
31	E Lupercio, B Uribe, Loop groupoids, gerbes, and twisted sectors on orbifolds, from: "Orbifolds in mathematics and physics" (editors A Adem, J Morava, Y Ruan), Contemp. Math. 310, Amer. Math. Soc. (2002) 163 MR1950946
32	E k M Moutuou, Twisted groupoid KR–theory, PhD thesis, Université de Lorraine (2012)
33	W F Reynolds, Twisted group algebras over arbitrary fields, Illinois J. Math. 15 (1971) 91 MR279209
34	D Rumynin, M B Young, Burnside rings for real 2–representation theory : the linear theory, Commun. Contemp. Math. 23 (2021) MR4289902
35	U Schreiber, C Schweigert, K Waldorf, Unoriented WZW models and holonomy of bundle gerbes, Comm. Math. Phys. 274 (2007) 31 MR2318847
36	E Sharpe, Analogues of discrete torsion for the M-theory three-form, Phys. Rev. D 68 (2003) MR2071752
37	E Sharpe, Discrete torsion, Phys. Rev. D 68 (2003) MR2071751
38	E Sharpe, Notes on discrete torsion in orientifolds, J. Geom. Phys. 61 (2011) 1017 MR2782477
39	C Vafa, Modular invariance and discrete torsion on orbifolds, Nuclear Phys. B 273 (1986) 592 MR850976
40	S Willerton, The twisted Drinfeld double of a finite group via gerbes and finite groupoids, Algebr. Geom. Topol. 8 (2008) 1419 MR2443249
41	E Witten, On flux quantization in M-theory and the effective action, J. Geom. Phys. 22 (1997) 1 MR1441697
42	E Witten, The “parity” anomaly on an unorientable manifold, Phys. Rev. B 94 (2016)
43	M B Young, Orientation twisted homotopy field theories and twisted unoriented Dijkgraaf–Witten theory, Comm. Math. Phys. 374 (2020) 1645 MR4076085
44	M B Young, Real representation theory of finite categorical groups, High. Struct. 5 (2021) 18 MR4367217