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arXiv · 2610.03608

The Squire complex and its extensions revisited

Elton Pasku
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Abstract

The Squier complex $\mathcal{D}(\cP)$ has been defined in \cite{LDHM1} as a combinatorial 2-complex. Also several extensions of $\mathcal{D}(\cP)$ are defined and used extensively in \cite{LDHM2}, \cite{SES} and \cite{EP}. Since the results obtained in those papers rely on the assumption that $\mathcal{D}(\cP)$ and its extensions in \cite{LDHM2} and \cite{SES} are CW-complexes of dimensions 2 and 3, respectively, and no proofs are given to support these preconditions, we provide the respective proofs in the present paper.

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Elton Pasku. 2026-10-02. The Squire complex and its extensions revisited. https://arxiv.org/abs/2610.03608

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