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Torsion in finite H-spaces and the homotopy of the three-sphere

Torsion in finite H-spaces and the homotopy of the three-sphere
Torsion in finite H-spaces and the homotopy of the three-sphere
Let X be a 2-connected p-local finite H-space with a single cell in dimension three. We give a simple cohomological criterion which distinguishes when the inclusion i: S 3 i ? X has the property that the loop of its three-connected cover is null homotopic. In particular, such a null homotopy implies that ? m (i)=0 for m?4 . Applications are made to Harper's rank 2 finite H -space and simple, simply-connected, compact Lie groups.
Beben, Piotr
a74d3e1f-52e0-4dc6-8f20-9c1628a20d2b
Theriault, Stephen
5e442ce4-8941-41b3-95f1-5e7562fdef80
Beben, Piotr
a74d3e1f-52e0-4dc6-8f20-9c1628a20d2b
Theriault, Stephen
5e442ce4-8941-41b3-95f1-5e7562fdef80

Beben, Piotr and Theriault, Stephen (2010) Torsion in finite H-spaces and the homotopy of the three-sphere. Homology, Homotopy and Applications, 12 (2).

Record type: Article

Abstract

Let X be a 2-connected p-local finite H-space with a single cell in dimension three. We give a simple cohomological criterion which distinguishes when the inclusion i: S 3 i ? X has the property that the loop of its three-connected cover is null homotopic. In particular, such a null homotopy implies that ? m (i)=0 for m?4 . Applications are made to Harper's rank 2 finite H -space and simple, simply-connected, compact Lie groups.

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Published date: 2010
Organisations: Mathematical Sciences

Identifiers

Local EPrints ID: 365620
URI: http://eprints.soton.ac.uk/id/eprint/365620
PURE UUID: 584c84a9-c182-43c1-aa54-0e967d0fe575
ORCID for Stephen Theriault: ORCID iD orcid.org/0000-0002-7729-5527

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Date deposited: 10 Jun 2014 15:22
Last modified: 07 Aug 2019 00:34

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Contributors

Author: Piotr Beben

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