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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 E 8 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 + 1 D
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