On the topological \(K\)-theory of twisted equivariant perfect complexes

DOI10.4310/HHA.2023.V25.N1.A9zbMATH Open1520.19010arXiv1901.06806MaRDI QIDQ6039227

Author name not available (Why is that?)

Publication date: 4 May 2023

Published in: Homology, Homotopy and Applications (Search for Journal in Brave)

Abstract: We construct a comparison map from the topological K-theory of the dg-category of twisted perfect complexes on certain global quotient stacks to twisted equivariant K-theory, generalizing constructions of Halpern-Leistner-Pomerleano and Moulinos. We prove that this map is an equivalence if a version of the projective bundle theorem holds for twisted equivariant K-theory. Along the way, we give a new proof of a theorem of Moulinos that the comparison map is an equivalence in the non-equivariant case.

Full work available at URL: https://arxiv.org/abs/1901.06806

zbMATH Keywords

twisted equivariant \(K\)-theorytopological \(K\)-theorydg-category

Mathematics Subject Classification ID

Equivariant (K)-theory (19L47) Twisted (K)-theory; differential (K)-theory (19L50) Derived categories, triangulated categories (18G80)

Related Items (4)

Equivariant chain complexes, twisted homology and relative minimality of arrangements ⋮ The Atiyah-Segal completion theorem in twisted \(K\)-theory ⋮ Twisted \(K\)-theory, \(K\)-homology, and bivariant Chern-Connes type character of some infinite dimensional spaces ⋮ Universal twist in equivariant K -theory for proper and discrete actions

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