Cohomology of Coxeter groupswith group ring coefficients: II
نویسندگان
چکیده
The cohomology of a group G with coefficients in a left G–module M is denoted H .GIM /. We are primarily interested in the case where M is the group ring, ZG . Since ZG is a G–bimodule, H .GIZG/ inherits the structure of a right G– module. When G is discrete and acts properly and cocompactly on a contractible CW complex , there is a natural topological interpretation for this cohomology group: H .GIZG/ŠH c ./, where H c . / denotes finitely supported cellular cohomology. The action of G on induces a right action on cohomology and the above isomorphism is one of right G–modules. For a general group G , not much is known about the G–module structure on H .GIZG/. For example, even in the above case where G acts properly and cocompactly on a contractible , we don’t believe it is known whether or not H .GIZG/ is always finitely generated as a G–module.
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