Volume 20, issue 3 (2020)

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Exponential functors, $R$–matrices and twists

Ulrich Pennig

Algebraic & Geometric Topology 20 (2020) 1279–1324
Bibliography
1 J F Adams, Infinite loop spaces, 90, Princeton Univ. Press (1978) MR505692
2 A Adem, J M Gómez, J A Lind, U Tillmann, Infinite loop spaces and nilpotent K–theory, Algebr. Geom. Topol. 17 (2017) 869 MR3623675
3 M Ando, A J Blumberg, D Gepner, M J Hopkins, C Rezk, An –categorical approach to R–line bundles, R–module Thom spectra, and twisted R–homology, J. Topol. 7 (2014) 869 MR3252967
4 M Ando, A J Blumberg, D Gepner, M J Hopkins, C Rezk, Units of ring spectra, orientations and Thom spectra via rigid infinite loop space theory, J. Topol. 7 (2014) 1077 MR3286898
5 M Atiyah, G Segal, Twisted K–theory, Ukr. Mat. Visn. 1 (2004) 287 MR2172633
6 M Atiyah, G Segal, Twisted K–theory and cohomology, from: "Inspired by S S Chern" (editor P A Griffiths), Nankai Tracts Math. 11, World Sci. (2006) 5 MR2307274
7 P Bouwknegt, A L Carey, V Mathai, M K Murray, D Stevenson, Twisted K–theory and K–theory of bundle gerbes, Comm. Math. Phys. 228 (2002) 17 MR1911247
8 A Buss, R Meyer, C Zhu, A higher category approach to twisted actions on C–algebras, Proc. Edinb. Math. Soc. 56 (2013) 387 MR3056650
9 M Dadarlat, U Pennig, Unit spectra of K–theory from strongly self-absorbing C–algebras, Algebr. Geom. Topol. 15 (2015) 137 MR3325734
10 M Dadarlat, U Pennig, A Dixmier–Douady theory for strongly self-absorbing C–algebras, J. Reine Angew. Math. 718 (2016) 153 MR3545881
11 P Donovan, M Karoubi, Graded Brauer groups and K–theory with local coefficients, Inst. Hautes Études Sci. Publ. Math. 38 (1970) 5 MR282363
12 D E Evans, T Gannon, Modular invariants and twisted equivariant K–theory, Commun. Number Theory Phys. 3 (2009) 209 MR2551893
13 D E Evans, U Pennig, Equivariant higher twisted K–theory of SU(n) for exponential functor twists, preprint (2019) arXiv:1906.08179
14 D S Freed, M J Hopkins, C Teleman, Loop groups and twisted K–theory, I, J. Topol. 4 (2011) 737 MR2860342
15 D S Freed, M J Hopkins, C Teleman, Loop groups and twisted K–theory, III, Ann. of Math. 174 (2011) 947 MR2831111
16 D S Freed, M J Hopkins, C Teleman, Loop groups and twisted K–theory, II, J. Amer. Math. Soc. 26 (2013) 595 MR3037783
17 B Harris, Bott periodicity via simplicial spaces, J. Algebra 62 (1980) 450 MR563240
18 A Kumjian, Fell bundles over groupoids, Proc. Amer. Math. Soc. 126 (1998) 1115 MR1443836
19 G Lechner, U Pennig, S Wood, Yang–Baxter representations of the infinite symmetric group, Adv. Math. 355 (2019) MR3994446
20 I G Macdonald, Symmetric functions and Hall polynomials, Clarendon (2015) MR3443860
21 J P May, The geometry of iterated loop spaces, 271, Springer (1972) MR0420610
22 J P May, K Ponto, More concise algebraic topology: localization, completion, and model categories, Univ. of Chicago Press (2012) MR2884233
23 E Meinrenken, The basic gerbe over a compact simple Lie group, Enseign. Math. 49 (2003) 307 MR2026898
24 M Murray, D Stevenson, The basic bundle gerbe on unitary groups, J. Geom. Phys. 58 (2008) 1571 MR2463811
25 A Okunkov, On representations of the infinite symmetric group, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. 240 (1997) 166 MR1691646
26 R S Palais, Homotopy theory of infinite dimensional manifolds, Topology 5 (1966) 1 MR189028
27 U Pennig, A non-commutative model for higher twisted K–theory, J. Topol. 9 (2016) 27 MR3465839
28 O Randal-Williams, “Group-completion”, local coefficient systems and perfection, Q. J. Math. 64 (2013) 795 MR3094500
29 C Rezk, The units of a ring spectrum and a logarithmic cohomology operation, J. Amer. Math. Soc. 19 (2006) 969 MR2219307
30 S Sagave, C Schlichtkrull, Group completion and units in –spaces, Algebr. Geom. Topol. 13 (2013) 625 MR3044590
31 C Schlichtkrull, Units of ring spectra and their traces in algebraic K–theory, Geom. Topol. 8 (2004) 645 MR2057776
32 D P Sullivan, Geometric topology : localization, periodicity and Galois symmetry (the 1970 MIT notes), 8, Springer (2005) MR2162361
33 C Teleman, K–theory and the moduli space of bundles on a surface and deformations of the Verlinde algebra, from: "Topology, geometry and quantum field theory" (editor U Tillmann), London Math. Soc. Lecture Note Ser. 308, Cambridge Univ. Press (2004) 358 MR2079380
34 E Thoma, Die unzerlegbaren, positiv-definiten Klassenfunktionen der abzählbar unendlichen, symmetrischen Gruppe, Math. Z. 85 (1964) 40 MR173169
35 K Waldorf, Multiplicative bundle gerbes with connection, Differential Geom. Appl. 28 (2010) 313 MR2610397
36 I Yokota, On the cellular decompositions of unitary groups, J. Inst. Polytech. Osaka City Univ. Ser. A 7 (1956) 39 MR84768