Segal's spectral sequence in twisted equivariant K-theory for proper and discrete actions

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 we recover known results when the twisting comes from finite order elements in discrete torsion.

arXiv comment25 pages. Corrected version. arXiv admin note: text overlap with arXiv:math/0411656 by other authors

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Cited by in corpus (9)

• Universal twist in Equivariant K-theory for proper and discrete actions
• Equivariant K-theory of compact Lie group actions with maximal rank isotropy
• Twisted equivariant K- Theory and K-Homology of Sl3(Z)
• Twisted equivariant K-theory of compact Lie group actions with maximal rank isotropy
• Bredon Cohomology, K theory and K homology of Pullbacks of groups
• The Completion Theorem in twisted equivariant $K$-Theory for proper and discrete actions
• Twisted Geometric K-homology for Proper actions of discrete groups
• Equivariant K-Theory of Central Extensions and Twisted Equivariant K-theory: Sl3(Z) and St3(Z)
• A Kunneth formula for Bredon cohomology of pullbacks and twisted K-theory of some 6-dimensional orbifolds