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Actions of Totally Disconnected Groups and Equivariant Singular Cohomology

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Abstract

In this work, we study the special properties of the equivariant singular cohomology of a G-space X, where G is a totally disconnected, locally compact group. We prove that any short exact sequence of coefficient systems for G, over a ring R, gives a long exact sequence of the associated equivariant singular cohomology modules. We establish the relationship between the ordinary singular cohomology modules and the equivariant singular cohomology modules with the natural contravariant coefficient system. Moreover, under some conditions, we give an isomorphism of the equivariant singular cohomology modules of the G-space X onto the ordinary singular cohomology modules of the orbit space X/G.

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Authors and Affiliations

  1. Department of Mathematics and statistics, University of Helsinki, P. O. Box 68, 00014, Helsinki, Finland

    Peilin Shi

  2. Department of Mathematics, Taiyuan University of Technology, Taiyuan, 030024, Shanxi, People’s Republic of China

    Peilin Shi

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  1. Peilin Shi
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Correspondence to Peilin Shi.

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Shi, P. Actions of Totally Disconnected Groups and Equivariant Singular Cohomology. Results. Math. 59, 63–81 (2011). https://doi.org/10.1007/s00025-010-0055-z

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  • DOI: https://doi.org/10.1007/s00025-010-0055-z

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