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arXiv · 1310.2315

Regular CW-complexes and poset resolutions of monomial ideals

Timothy B. P. Clark·Alexandre Tchernev
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Abstract

We use the natural homeomorphism between a regular CW-complex X and its face poset P_X to establish a canonical isomorphism between the cellular chain complex of X and the result of applying the poset construction of arXiv:0806.4532v1 to P_X. For a monomial ideal whose free resolution is supported on a regular CW-complex, this isomorphism allows the free resolution of the ideal to be realized as a CW-poset resolution. Conversely, any CW-poset resolution of a monomial ideal gives rise to a resolution supported on a regular CW-complex.

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Timothy B. P. Clark, Alexandre Tchernev. 2013-10-09. Regular CW-complexes and poset resolutions of monomial ideals. https://arxiv.org/abs/1310.2315

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