Actions of Totally Disconnected Groups and Equivariant Singular Cohomology

作者：Shi Peilin^*

来源：Results in Mathematics, 2011, 59(1-2): 63-81.

DOI：10.1007/s00025-010-0055-z

• Totally disconnected locally compact group
• action
• equivariant singular cohomology
• exact sequence

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.

• 出版日期2011-2
• 单位太原理工大学