Cohen-Macaulay and Gorenstein complexes from a topological point of view

Details Cohen-Macaulay and Gorenstein complexes from a topological point of view Cohen-Macaulay and Gorenstein complexes from a topological point of view

2005-08-16

arxiv.org/abs/math/0508292v1

Mathematics

Algebraic Topology

26 pages

Scientific paper

The main invariant to study the combinatorics of a simplicial complex $K$ is the associated face ring or Stanley-Reisner algebra. Reisner respectively Stanley explained in which sense Cohen-Macaulay and Gorenstein properties of the face ring are reflected by geometric and/or combinatoric properties of the simplicial complex. We give a new proof for these result by homotopy theoretic methods and constructions. Our approach is based on ideas used very successfully in the analysis of the homotopy theory of classifying spaces.

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