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Modular representations and the homotopy of low rank p-local CW-complexes

Modular representations and the homotopy of low rank p-local CW-complexes
Modular representations and the homotopy of low rank p-local CW-complexes
Fix an odd prime p and let X be the p-localization of a finite suspended CW-complex. Given certain conditions on the reduced mod-p homology H˜?(X;Zp) of X, we use a decomposition of ??X due to the second author and computations in modular representation theory to show there are arbitrarily large integers i such that ?? i X is a homotopy retract of ??X. This implies the stable homotopy groups of ?X are in a certain sense retracts of the unstable homotopy groups, and by a result of Stanley, one can confirm the Moore conjecture for ?X. Under additional assumptions on H˜?(X;Zp), we generalize a result of Cohen and Neisendorfer to produce a homotopy decomposition of ??X that has infinitely many finite H-spaces as factors.
loop space decompositions, finite CW-complexes, modular representations
0025-5874
735-751
Beben, Piotr
a74d3e1f-52e0-4dc6-8f20-9c1628a20d2b
Wu, Jie
541b9f29-928c-4fbd-9697-2f567d76feb6
Beben, Piotr
a74d3e1f-52e0-4dc6-8f20-9c1628a20d2b
Wu, Jie
541b9f29-928c-4fbd-9697-2f567d76feb6

Beben, Piotr and Wu, Jie (2013) Modular representations and the homotopy of low rank p-local CW-complexes. Mathematische Zeitschrift, 273 (3-4), 735-751. (doi:10.1007/s00209-012-1027-7).

Record type: Article

Abstract

Fix an odd prime p and let X be the p-localization of a finite suspended CW-complex. Given certain conditions on the reduced mod-p homology H˜?(X;Zp) of X, we use a decomposition of ??X due to the second author and computations in modular representation theory to show there are arbitrarily large integers i such that ?? i X is a homotopy retract of ??X. This implies the stable homotopy groups of ?X are in a certain sense retracts of the unstable homotopy groups, and by a result of Stanley, one can confirm the Moore conjecture for ?X. Under additional assumptions on H˜?(X;Zp), we generalize a result of Cohen and Neisendorfer to produce a homotopy decomposition of ??X that has infinitely many finite H-spaces as factors.

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More information

e-pub ahead of print date: 20 April 2012
Published date: April 2013
Keywords: loop space decompositions, finite CW-complexes, modular representations
Organisations: Mathematical Sciences

Identifiers

Local EPrints ID: 365617
URI: https://eprints.soton.ac.uk/id/eprint/365617
ISSN: 0025-5874
PURE UUID: fb04bba3-7a6a-405b-8fed-a39f5c152406

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Date deposited: 10 Jun 2014 15:14
Last modified: 18 Jul 2017 02:19

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