Stabilization of Poincare duality complexes and homotopy gyrations
Stabilization of Poincare duality complexes and homotopy gyrations
Stabilization of manifolds by a product of spheres or a projective space is important in geometry. There has been considerable recent work that studies the homotopy theory of stabilization for connected manifolds. This paper generalizes that work by developing new methods that allow for a generalization to stabilization of Poincare Duality complexes. This includes the systematic study of a homotopy theoretic generalization of a gyration, obtained from a type of surgery in the manifold case. In particular, for a fixed Poincare Duality complex, a criterion is given for the possible homotopy types of gyrations and shows there are only finitely many.
loop space decomposition, connected sum, fibration
Theriault, Stephen
5e442ce4-8941-41b3-95f1-5e7562fdef80
Huang, Ruizhi
e6cc7bca-a048-4475-b6ca-73a9cf33431f
Theriault, Stephen
5e442ce4-8941-41b3-95f1-5e7562fdef80
Huang, Ruizhi
e6cc7bca-a048-4475-b6ca-73a9cf33431f
Theriault, Stephen and Huang, Ruizhi
(2026)
Stabilization of Poincare duality complexes and homotopy gyrations.
Journal of the London Mathematical Society.
(In Press)
Abstract
Stabilization of manifolds by a product of spheres or a projective space is important in geometry. There has been considerable recent work that studies the homotopy theory of stabilization for connected manifolds. This paper generalizes that work by developing new methods that allow for a generalization to stabilization of Poincare Duality complexes. This includes the systematic study of a homotopy theoretic generalization of a gyration, obtained from a type of surgery in the manifold case. In particular, for a fixed Poincare Duality complex, a criterion is given for the possible homotopy types of gyrations and shows there are only finitely many.
Text
Stabilization revised
- Accepted Manuscript
More information
Accepted/In Press date: 20 March 2026
Keywords:
loop space decomposition, connected sum, fibration
Identifiers
Local EPrints ID: 511008
URI: http://eprints.soton.ac.uk/id/eprint/511008
ISSN: 0024-6107
PURE UUID: fa301873-89ba-49bf-abed-1baa20795e54
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Date deposited: 28 Apr 2026 17:02
Last modified: 29 Apr 2026 01:47
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Author:
Ruizhi Huang
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