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Loop spaces of n-dimensional Poincaré duality complexes whose (n-1)-skeleton is a co-H-space

Loop spaces of n-dimensional Poincaré duality complexes whose (n-1)-skeleton is a co-H-space
Loop spaces of n-dimensional Poincaré duality complexes whose (n-1)-skeleton is a co-H-space
Under certain hypotheses, we prove a loop space decomposition for simply-connected Poincaré Duality complexes of dimension n whose (n-1)-skeleton is a co-H-space. This unifies many known decompositions obtained in different contexts and establishes many new families of examples. As consequences, we show that such a looped Poincaré Duality complex retracts off the loops of its (n-1)-skeleton and describe its homology as a one-relator algebra.
Poincaré Duality complex, co-H-space, loop space, homotopy type
0002-9947
Stanton, Lewis
bb6aed52-6a94-403f-a87e-5d7b7a6c8152
Theriault, Stephen
5e442ce4-8941-41b3-95f1-5e7562fdef80
Stanton, Lewis
bb6aed52-6a94-403f-a87e-5d7b7a6c8152
Theriault, Stephen
5e442ce4-8941-41b3-95f1-5e7562fdef80

Stanton, Lewis and Theriault, Stephen (2025) Loop spaces of n-dimensional Poincaré duality complexes whose (n-1)-skeleton is a co-H-space. Transactions of the American Mathematical Society. (In Press)

Record type: Article

Abstract

Under certain hypotheses, we prove a loop space decomposition for simply-connected Poincaré Duality complexes of dimension n whose (n-1)-skeleton is a co-H-space. This unifies many known decompositions obtained in different contexts and establishes many new families of examples. As consequences, we show that such a looped Poincaré Duality complex retracts off the loops of its (n-1)-skeleton and describe its homology as a one-relator algebra.

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Accepted/In Press date: 16 June 2025
Keywords: Poincaré Duality complex, co-H-space, loop space, homotopy type
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Identifiers

Local EPrints ID: 503263
URI: http://eprints.soton.ac.uk/id/eprint/503263
ISSN: 0002-9947
PURE UUID: b43d9091-58b9-4aca-9e89-b065cc39e5fd
ORCID for Lewis Stanton: ORCID iD orcid.org/0000-0003-4662-054X
ORCID for Stephen Theriault: ORCID iD orcid.org/0000-0002-7729-5527

Catalogue record

Date deposited: 25 Jul 2025 16:45
Last modified: 26 Jul 2025 02:08

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Contributors

Author: Lewis Stanton ORCID iD
Author: Stephen Theriault ORCID iD

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