Anick spaces and Kac–Moody groups

Theriault, Stephen; Wu, Jie

doi:10.2140/agt.2018.18.4305

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Anick spaces and Kac–Moody groups

Stephen Theriault and Jie Wu

Algebraic & Geometric Topology 18 (2018) 4305–4328

DOI: 10.2140/agt.2018.18.4305

Abstract

For primes $p \geq 5$ we prove an approximation to Cohen, Moore and Neisendorfer’s conjecture that the loops on an Anick space retracts off the double loops on a mod- $p$ Moore space. The approximation is then used to answer a question posed by Kitchloo regarding the topology of Kac–Moody groups. We show that, for certain rank- $2$ Kac–Moody groups $K$ , the based loops on $K$ is $p$ –locally homotopy equivalent to the product of the loops on a $3$ –sphere and the loops on an Anick space.

Keywords

Anick space, Moore space, Kac–Moody group

Mathematical Subject Classification 2010

Primary: 55P35

Secondary: 55P15, 57T20

References

Publication

Received: 31 March 2018

Revised: 10 June 2018

Accepted: 21 June 2018

Published: 11 December 2018

Authors

Stephen Theriault
Mathematical Sciences University of Southampton Southampton United Kingdom

Jie Wu
Department of Mathematics National University of Singapore Singapore

Volume 18, issue 7 (2018)