Anick spaces and Kac–Moody groups

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.