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

For primes p 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.

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Anick space, Moore space, Kac–Moody group
Mathematical Subject Classification 2010
Primary: 55P35
Secondary: 55P15, 57T20
Received: 31 March 2018
Revised: 10 June 2018
Accepted: 21 June 2018
Published: 11 December 2018
Stephen Theriault
Mathematical Sciences
University of Southampton
United Kingdom
Jie Wu
Department of Mathematics
National University of Singapore