Segal's Spectral Sequence in Twisted Equivariant K-theory for Proper and Discrete Actions. Issue 1 (23rd January 2018)

• Record Type: Journal Article
• Authors: Bárcenas, Noé; Espinoza, Jesús; Uribe, Bernardo; Velásquez, Mario
• Is Part Of: Proceedings of the Edinburgh Mathematical Society. Volume 61:Issue 1(2018)
• Page Start: 121
• Page End: 150
• Publication Date: 2018-01-23
• Subjects: twisted equivariant K-theory, -- Bredon cohomology, -- proper actions, -- twisted representations; Primary 19L47, -- 19L50, -- 55N91, -- Secondary 18G40; Mathematics -- Periodicals; 510
• DOI: 10.1017/S0013091517000281
• Languages: English
• ISSNs: 0013-0915

Abstract

Abstract: We use a spectral sequence developed by Graeme Segal in order to understand the twisted G -equivariant K-theory for proper and discrete actions. We show that the second page of this spectral sequence is isomorphic to a version of Bredon cohomology with local coefficients in twisted representations. We furthermore explain some phenomena concerning the third differential of the spectral sequence, and recover known results when the twisting comes from finite order elements in discrete torsion.