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arXiv · 1206.1819

Combinatorial resolutions of multigraded modules and multipersistent homology

Wojciech Chacholski·Martina Scolamiero·Francesco Vaccarino
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Abstract

Let $ R=k[x_1...x_r]$ and $M$ a multigraded $R-$module. In this work we interpret $M$ as a multipersistent homology module and give a multigraded resolution of it. The construction involves cellular resolutions of monomial ideals and reflects the combinatorial structure of multipersistence homology modules. In the one critical case, a multifiltration is represented by a labelled cellular complex. A multipersistence homology module measures the defect of acyclicity of the associated multigraded cellular chain complex.

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Wojciech Chacholski, Martina Scolamiero, Francesco Vaccarino. 2015-12-21. Combinatorial resolutions of multigraded modules and multipersistent homology. https://arxiv.org/abs/1206.1819

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