Volume 18, issue 7 (2018)

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Anick spaces and Kac–Moody groups

Stephen Theriault and Jie Wu

Algebraic & Geometric Topology 18 (2018) 4305–4328
Abstract

For primes $p\ge 5$ 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
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