Algebraic & Geometric Topology

Anick spaces and Kac–Moody groups

Stephen Theriault and Jie Wu

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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.

Article information

Algebr. Geom. Topol., Volume 18, Number 7 (2018), 4305-4328.

Received: 31 March 2018
Revised: 10 June 2018
Accepted: 21 June 2018
First available in Project Euclid: 18 December 2018

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55P35: Loop spaces
Secondary: 55P15: Classification of homotopy type 57T20: Homotopy groups of topological groups and homogeneous spaces

Anick space Moore space Kac–Moody group


Theriault, Stephen; Wu, Jie. Anick spaces and Kac–Moody groups. Algebr. Geom. Topol. 18 (2018), no. 7, 4305--4328. doi:10.2140/agt.2018.18.4305.

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