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Loop space decompositions of moment-angle complexes associated to two-dimensional simplicial complexes

Part of: Homotopy theory

Published online by Cambridge University Press:  07 April 2025

Lewis Stanton Open the ORCID record for Lewis Stanton [Opens in a new window]
Lewis Stanton*
Affiliation:
School of Mathematical Sciences, University of Southampton, Southampton, SO17 1BJ, United Kingdom
*
Email: [email protected]
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Abstract

We show that the loop space of a moment-angle complex associated to a two-dimensional simplicial complex decomposes as a finite type product of spheres, loops on spheres and certain indecomposable spaces which appear in the loop space decomposition of Moore spaces. We also give conditions on certain subcomplexes under which, localised away from sufficiently many primes, the loop space of a moment-angle complex decomposes as a finite type product of spheres and loops on spheres.

Keywords

homotopy typeloop spacepolyhedral product

MSC classification

Primary: 55P15: Classification of homotopy type
Secondary: 55P35: Loop spaces
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , First View , pp. 1 - 23
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society.

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