Suspension splittings and James-Hopf invariants for retracts of the loops on co-H-spaces
Suspension splittings and James-Hopf invariants for retracts of the loops on co-H-spaces
James constructed a functorial homotopy decomposition X ' W1 n=1 X (n) for path-connected, pointed CW -complexes X. We generalize this to a functorial decomposition of A where A is any functorial retract of a looped co-H-space. This is used to construct Hopf invariants in a more general context. In addition, when A = Y is the loops on a co-H-space, we show that the wedge summands of Y further functorially decompose by using an action of an appropriate symmetric group.
co-h-space, functorial decomposition, hopf invariant
87-108
Grbić, J.
daaea124-d4cc-4818-803a-2b0cb4362175
Theriault, S.
5e442ce4-8941-41b3-95f1-5e7562fdef80
Wu, J.
5a0119e5-a760-4ff5-90b9-ec69926ce501
February 2014
Grbić, J.
daaea124-d4cc-4818-803a-2b0cb4362175
Theriault, S.
5e442ce4-8941-41b3-95f1-5e7562fdef80
Wu, J.
5a0119e5-a760-4ff5-90b9-ec69926ce501
Grbić, J., Theriault, S. and Wu, J.
(2014)
Suspension splittings and James-Hopf invariants for retracts of the loops on co-H-spaces.
Proceedings of the Royal Society of Edinburgh Section A Mathematics, 144 (1), .
(doi:10.1017/S0308210512000480).
Abstract
James constructed a functorial homotopy decomposition X ' W1 n=1 X (n) for path-connected, pointed CW -complexes X. We generalize this to a functorial decomposition of A where A is any functorial retract of a looped co-H-space. This is used to construct Hopf invariants in a more general context. In addition, when A = Y is the loops on a co-H-space, we show that the wedge summands of Y further functorially decompose by using an action of an appropriate symmetric group.
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Accepted/In Press date: 20 December 2012
e-pub ahead of print date: 30 January 2014
Published date: February 2014
Keywords:
co-h-space, functorial decomposition, hopf invariant
Organisations:
Pure Mathematics
Identifiers
Local EPrints ID: 341248
URI: http://eprints.soton.ac.uk/id/eprint/341248
ISSN: 0308-2105
PURE UUID: 7aff90d7-1741-43bc-9fa2-285bc21ae122
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Date deposited: 18 Jul 2012 13:22
Last modified: 15 Mar 2024 03:45
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Author:
J. Wu
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