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<p>We develop a theory for deforming an arbitrary free complex into a differential module. The theory uses an iterative approach to parameterize the deformations and obstructions in terms of certain <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\operatorname {Ext}\)</EquationSource> </InlineEquation> 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.</p>

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Differential modules and deformations of free complexes

  • 期刊论文

  • 发表日期：

    2026年1月16日

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  • Maya Banks,
  • Keller VandeBogert

摘要

We develop a theory for deforming an arbitrary free complex into a differential module. The theory uses an iterative approach to parameterize the deformations and obstructions in terms of certain \(\operatorname {Ext}\) 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.