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The Kahn-Priddy Theorem and the homotopy of the three-sphere

The Kahn-Priddy Theorem and the homotopy of the three-sphere
The Kahn-Priddy Theorem and the homotopy of the three-sphere
Let p be an odd prime. The least nontrivial p-torsion homotopy group of S^{3} occurs in dimension 2p and is of order p. This induces a map f\colon P^2p+1(p)\rightarrow S^3, where P^2p+1(p) is a mod-p Moore space. An important conjecture related to the Kahn-Priddy Theorem is that the double loops on the three-connected cover of f has a right homotopy inverse. We prove a weaker but still useful property: if X is the cofiber of f, then the double loop on the three-connected cover of the inclusion S^3\rightarrow X is null homotopic.
0002-9939
711-723
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 (2013) The Kahn-Priddy Theorem and the homotopy of the three-sphere. Proceedings of the American Mathematical Society, 141 (2), 711-723.

Record type: Article

Abstract

Let p be an odd prime. The least nontrivial p-torsion homotopy group of S^{3} occurs in dimension 2p and is of order p. This induces a map f\colon P^2p+1(p)\rightarrow S^3, where P^2p+1(p) is a mod-p Moore space. An important conjecture related to the Kahn-Priddy Theorem is that the double loops on the three-connected cover of f has a right homotopy inverse. We prove a weaker but still useful property: if X is the cofiber of f, then the double loop on the three-connected cover of the inclusion S^3\rightarrow X is null homotopic.

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More information

e-pub ahead of print date: 12 June 2012
Published date: February 2013
Organisations: Mathematical Sciences

Identifiers

Local EPrints ID: 365619
URI: https://eprints.soton.ac.uk/id/eprint/365619
ISSN: 0002-9939
PURE UUID: 68385f1f-2174-4aa1-a881-c6d674f8d318
ORCID for Stephen Theriault: ORCID iD orcid.org/0000-0002-7729-5527

Catalogue record

Date deposited: 10 Jun 2014 15:19
Last modified: 09 Oct 2018 00:30

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