A method for integral cohomology of posets

Details A method for integral cohomology of posets A method for integral cohomology of posets

2007-06-14

arxiv.org/abs/0706.2118v1

Mathematics

Algebraic Topology

35 pages

Scientific paper

We present a method to compute integral cohomology of posets. This toolbox is applicable as soon as the sub-posets under each object possess certain structure. This is the case for simplicial complexes and simplex-like posets. The method is based on homological algebra arguments in the category of functors and on a spectral sequence built upon the poset. We show its relation to discrete Morse theory. As application we give an alternative proof of Webb's conjecture for saturated fusion systems and we compute the cohomology of Coxeter complexes for finite and infinite Coxeter groups.

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