## Algebraic & Geometric Topology

### Anick spaces and Kac–Moody groups

#### Abstract

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

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

Dates
Revised: 10 June 2018
Accepted: 21 June 2018
First available in Project Euclid: 18 December 2018

https://projecteuclid.org/euclid.agt/1545102072

Digital Object Identifier
doi:10.2140/agt.2018.18.4305

Mathematical Reviews number (MathSciNet)
MR3892246

Zentralblatt MATH identifier
07006392

#### Citation

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. https://projecteuclid.org/euclid.agt/1545102072

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