Volume 20, issue 3 (2020)

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

Volume 25
Issue 6, 3145–3787
Issue 5, 2527–3144
Issue 4, 1917–2526
Issue 3, 1265–1915
Issue 2, 645–1264
Issue 1, 1–644

Volume 24, 9 issues

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
 
Author index
To appear
 
Other MSP journals
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