Homotopy theoretic properties of gyrations
Homotopy theoretic properties of gyrations
Let M be a simply-connected n-dimensional manifold with the property that the attaching map for the n-cell is inert, which means that the inclusion of the (n − 1)-skeleton has a right homotopy inverse after looping. We show that a type of surgery on M × S^{k−1} producing a manifold called a gyration preserves the inertness property. The method generalizes to Poincare Duality complexes and also recovers by different means a known homotopy equivalence for the based loops of the gyration. The underlying method is quite general and should have applications elsewhere.
gyration, inert attaching map, loop space decomposition
Theriault, Stephen
5e442ce4-8941-41b3-95f1-5e7562fdef80
Theriault, Stephen
5e442ce4-8941-41b3-95f1-5e7562fdef80
Theriault, Stephen
(2026)
Homotopy theoretic properties of gyrations.
Pacific Journal of Mathematics.
(In Press)
Abstract
Let M be a simply-connected n-dimensional manifold with the property that the attaching map for the n-cell is inert, which means that the inclusion of the (n − 1)-skeleton has a right homotopy inverse after looping. We show that a type of surgery on M × S^{k−1} producing a manifold called a gyration preserves the inertness property. The method generalizes to Poincare Duality complexes and also recovers by different means a known homotopy equivalence for the based loops of the gyration. The underlying method is quite general and should have applications elsewhere.
Text
gyration inert revised
- Accepted Manuscript
More information
Accepted/In Press date: 10 June 2026
Keywords:
gyration, inert attaching map, loop space decomposition
Identifiers
Local EPrints ID: 513729
URI: https://eprints.soton.ac.uk/id/eprint/513729
ISSN: 0030-8730
PURE UUID: b653b202-1fc9-4fbf-b334-c269460e207d
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Date deposited: 25 Aug 2026 16:40
Last modified: 25 Sep 2026 04:01
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