Homological Finiteness Properties of Groups

Part of the Graduate Texts in Mathematics book series (GTM, volume 243)

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.


Universal Cover Morse Theory Morse Function Free Resolution Cubical Complex 
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© Springer Science+Business Media, LLC 2008

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