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Twisted differential cohomology

Ulrich Bunke and Thomas Nikolaus

Algebraic & Geometric Topology 19 (2019) 1631–1710
1 M Ando, A J Blumberg, D Gepner, Twists of K–theory and TMF, from: "Superstrings, geometry, topology, and C–algebras" (editors R S Doran, G Friedman, J Rosenberg), Proc. Sympos. Pure Math. 81, Amer. Math. Soc. (2010) 27 MR2681757
2 M Ando, A J Blumberg, D Gepner, Parametrized spectra, multiplicative Thom spectra and the twisted Umkehr map, Geom. Topol. 22 (2018) 3761 MR3890766
3 B Antieau, D Gepner, Brauer groups and étale cohomology in derived algebraic geometry, Geom. Topol. 18 (2014) 1149 MR3190610
4 B Antieau, D Gepner, J M Gómez, Actions of K(π,n) spaces on K–theory and uniqueness of twisted K–theory, Trans. Amer. Math. Soc. 366 (2014) 3631 MR3192610
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 : a memorial volume in honor of a great mathematician" (editor P A Griffiths), Nankai Tracts Math. 11, World Sci. (2006) 5 MR2307274
7 N Barcenas, M Velasquez, Twisted equivariant K–theory and K–homology of Sl3(), preprint (2013) arXiv:1304.0939
8 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
9 U Bunke, Differential cohomology, lecture notes (2012) arXiv:1208.3961
10 U Bunke, D Gepner, Differential function spectra, the differential Becker–Gottlieb transfer, and applications to differential algebraic K–theory, preprint (2013) arXiv:1306.0247
11 U Bunke, T Nikolaus, M Völkl, Differential cohomology theories as sheaves of spectra, J. Homotopy Relat. Struct. 11 (2016) 1 MR3462099
12 U Bunke, T Schick, On the topology of T–duality, Rev. Math. Phys. 17 (2005) 77 MR2130624
13 U Bunke, T Schick, Smooth K–theory, from: "De probabilité à géométrie, II" (editors X Dai, R Léandre, X Ma, W Zhang), Astérisque 328, Soc. Mat. de France (2009) 45 MR2664467
14 A L Carey, J Mickelsson, B L Wang, Differential twisted K–theory and applications, J. Geom. Phys. 59 (2009) 632 MR2518992
15 D Cisinski, Higher categories and homotopical algebra, book project (2019)
16 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
17 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, Int. (2011) 99 MR2815726
18 P Donovan, M Karoubi, Graded Brauer groups and K–theory with local coefficients, Inst. Hautes Études Sci. Publ. Math. 38 (1970) 5 MR0282363
19 D S Freed, Dirac charge quantization and generalized differential cohomology, from: "Surveys in differential geometry" (editor S T Yau), Surv. Differ. Geom. 7, Int. (2000) 129 MR1919425
20 D S Freed, M Hopkins, On Ramond–Ramond fields and K–theory, J. High Energy Phys. (2000) MR1769477
21 D S Freed, M J Hopkins, C Teleman, Loop groups and twisted K–theory, I, J. Topol. 4 (2011) 737 MR2860342
22 D S Freed, M J Hopkins, C Teleman, Loop groups and twisted K–theory, III, Ann. of Math. 174 (2011) 947 MR2831111
23 D S Freed, M J Hopkins, C Teleman, Loop groups and twisted K–theory, II, J. Amer. Math. Soc. 26 (2013) 595 MR3037783
24 K Gomi, Mickelsson’s twisted K–theory invariant and its generalizations, preprint (2013) arXiv:1303.5159
25 K Gomi, Y Terashima, Chern–Weil construction for twisted K–theory, Comm. Math. Phys. 299 (2010) 225 MR2672802
26 D Grady, H Sati, Twisted differential generalized cohomology theories and their Atiyah–Hirzebruch spectral sequence, preprint (2017) arXiv:1711.06650
27 M Groth, A short course on –categories, preprint (2010) arXiv:1007.2925
28 A J Harju, Twisted K–theory constructions in the case of a decomposable Dixmier–Douady class, II : Topological and equivariant models, J. Geom. Phys. 82 (2014) 46 MR3206639
29 A J Harju, J Mickelsson, Twisted K–theory constructions in the case of a decomposable Dixmier–Douady class, J. K–Theory 14 (2014) 247 MR3264263
30 V Hinich, Homological algebra of homotopy algebras, Comm. Algebra 25 (1997) 3291 MR1465117
31 M J Hopkins, M Mahowald, H Sadofsky, Constructions of elements in Picard groups, from: "Topology and representation theory" (editors E M Friedlander, M E Mahowald), Contemp. Math. 158, Amer. Math. Soc. (1994) 89 MR1263713
32 M J Hopkins, I M Singer, Quadratic functions in geometry, topology, and M-theory, J. Differential Geom. 70 (2005) 329 MR2192936
33 J Lurie, Higher topos theory, 170, Princeton Univ. Press (2009) MR2522659
34 J Lurie, Higher algebra, book project (2011)
35 J Maldacena, G Moore, N Seiberg, D–brane instantons and K–theory charges, J. High Energy Phys. (2001) MR1877986
36 V Mathai, D Stevenson, Chern character in twisted K–theory : equivariant and holomorphic cases, Comm. Math. Phys. 236 (2003) 161 MR1977885
37 V Mathai, D Stevenson, On a generalized Connes–Hochschild–Kostant–Rosenberg theorem, Adv. Math. 200 (2006) 303 MR2200848
38 A Mathew, L Meier, Affineness and chromatic homotopy theory, J. Topol. 8 (2015) 476 MR3356769
39 J P May, J Sigurdsson, Parametrized homotopy theory, 132, Amer. Math. Soc. (2006) MR2271789
40 J Mickelsson, J P Pellonpää, Families index theorem in supersymmetric WZW model and twisted K–theory : the SU(2) case, Comm. Math. Phys. 271 (2007) 775 MR2291795
41 J W Milnor, J C Moore, On the structure of Hopf algebras, Ann. of Math. 81 (1965) 211 MR0174052
42 T Nikolaus, U Schreiber, D Stevenson, Principal –bundles : general theory, J. Homotopy Relat. Struct. 10 (2015) 749 MR3423073
43 S Sagave, Spectra of units for periodic ring spectra and group completion of graded E spaces, Algebr. Geom. Topol. 16 (2016) 1203 MR3493419
44 U Schreiber, Differential cohomology in a cohesive –topos, preprint (2013) arXiv:1310.7930
45 B Shipley, H–algebra spectra are differential graded algebras, Amer. J. Math. 129 (2007) 351 MR2306038
46 J Simons, D Sullivan, Structured vector bundles define differential K–theory, from: "Quanta of maths" (editors E Blanchard, D Ellwood, M Khalkhali, M Marcolli, S Popa), Clay Math. Proc. 11, Amer. Math. Soc. (2010) 579 MR2732065
47 J L Tu, P Xu, Chern character for twisted K–theory of orbifolds, Adv. Math. 207 (2006) 455 MR2271013
48 J L Tu, P Xu, C Laurent-Gengoux, Twisted K–theory of differentiable stacks, Ann. Sci. École Norm. Sup. 37 (2004) 841 MR2119241