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

Dietrich Notbohm

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

Dietrich Notbohm

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Abstract

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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Dietrich Notbohm. 2005-08-16. Cohen-Macaulay and Gorenstein complexes from a topological point of view. https://arxiv.org/abs/math/0508292

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