An analogue of Ganea's Theorem for connected sums
An analogue of Ganea's Theorem for connected sums
Let M and N be simply-connected n-dimensional Poincare Duality complexes. A condition is given on M and N which allows for the based loops on the connected sum M#N to be expressed as a product of the based loops on M, the based loops on N, and an explicitly identified complementary factor. This is analogous to Ganea’s decomposition of the based loops on a wedge. A generalization is given for a connected sum of k Poincare Duality complexes for any k ≥ 2. The required condition holds, for instance, for products of spheres. Examples are given that are of particular interest in toric topology.
loop space decomposition, connected sum, moment-angle manifold
Theriault, Stephen
5e442ce4-8941-41b3-95f1-5e7562fdef80
Theriault, Stephen
5e442ce4-8941-41b3-95f1-5e7562fdef80
Theriault, Stephen
(2025)
An analogue of Ganea's Theorem for connected sums.
Annales Mathématiques du Quebec.
(In Press)
Abstract
Let M and N be simply-connected n-dimensional Poincare Duality complexes. A condition is given on M and N which allows for the based loops on the connected sum M#N to be expressed as a product of the based loops on M, the based loops on N, and an explicitly identified complementary factor. This is analogous to Ganea’s decomposition of the based loops on a wedge. A generalization is given for a connected sum of k Poincare Duality complexes for any k ≥ 2. The required condition holds, for instance, for products of spheres. Examples are given that are of particular interest in toric topology.
Text
Ganea conn sum revised
- Accepted Manuscript
Restricted to Repository staff only until 4 June 2026.
Available under License Other.
Request a copy
More information
Accepted/In Press date: 4 June 2025
Keywords:
loop space decomposition, connected sum, moment-angle manifold
Identifiers
Local EPrints ID: 503077
URI: http://eprints.soton.ac.uk/id/eprint/503077
ISSN: 2195-4755
PURE UUID: 5e18b09b-c026-4652-87d1-54326f25824b
Catalogue record
Date deposited: 21 Jul 2025 16:43
Last modified: 22 Jul 2025 01:47
Export record
Download statistics
Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.
View more statistics
