Homological Finiteness Properties of Groups
Here we introduce homology of groups and homological finiteness properties. The first two sections provide homological analogs of some of the topics in Chapter 7. A free (or projective) resolution of the trivial RG-module R plays the role of the universal cover of a K (G, 1)-complex. The properties FP n and cohomological dimension are analogous to F n and geometric dimension. This leads us to the Bestvina-Brady Theorem, which gives a method of constructing groups G for which the homological and topological properties are stubly different.
KeywordsUniversal Cover Morse Theory Morse Function Free Resolution Cubical Complex
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