Differential modules and Deformations of Free Complexes

Maya Banks; Keller VandeBogert

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arXiv · 2308.01973

Differential modules and Deformations of Free Complexes

Maya Banks·Keller VandeBogert

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Abstract

We classify (up to quasi-isomorphism) the free differential modules whose homology is equal to a given module $M$ by developing a theory for deforming an arbitrary free complex into a differential module. We use an iterative approach to parameterize the deformations and obstructions in terms of certain Ext groups, giving an algorithmic realization of a result of Brown-Erman. We apply this theory to study certain rigidity properties of free resolutions and related rank conjectures.

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Maya Banks, Keller VandeBogert. 2023-08-03. Differential modules and Deformations of Free Complexes. https://arxiv.org/abs/2308.01973

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