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Segal's Spectral Sequence in Twisted Equivariant K-theory for Proper and Discrete Actions

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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… Click to show full 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.

Keywords: twisted equivariant; spectral sequence; equivariant theory; theory proper; sequence; proper discrete

Journal Title: Proceedings of the Edinburgh Mathematical Society
Year Published: 2018

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