PreprintarXiv licencearXiv
The Squire complex and its extensions revisited
Abstract
The Squier complex π(cP) has been defined in \cite{LDHM1} as a combinatorial 2-complex. Also several extensions of π(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 π(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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BibTeX
@misc{pasku2026squire,
title = {{The Squire complex and its extensions revisited}},
author = {Elton Pasku},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03608},
eprint = {2610.03608},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03608},
}
RIS
TY - UNPB
TI - The Squire complex and its extensions revisited
AU - Elton Pasku
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.03608
UR - https://arxiv.org/abs/2610.03608
AB - The Squier complex π(cP) has been defined in \cite{LDHM1} as a combinatorial 2-complex. Also several extensions of π(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 π(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.
ER -