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arXiv · 2405.05873

Duality for Cohen--Macaulay Complexes through Combinatorial Sheaves

Richard D. Wade·Thomas A. Wasserman
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Abstract

We prove a duality theorem for Cohen--Macaulay simplicial complexes. This is a generalisation of Poincar\'e Duality, framed in the language of combinatorial sheaves. Our treatment is self-contained and accessible for readers with a working knowledge of simplicial complexes and (co)homology. The main motivation is a link with Bieri-Eckmann duality for discrete groups, which is explored in a companion paper.

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Richard D. Wade, Thomas A. Wasserman. 2024-05-09. Duality for Cohen--Macaulay Complexes through Combinatorial Sheaves. https://arxiv.org/abs/2405.05873

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