For primes 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- 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- Kac–Moody groups , the based loops on is –locally homotopy equivalent to the product of the loops on a –sphere and the loops on an Anick space.
"Anick spaces and Kac–Moody groups." Algebr. Geom. Topol. 18 (7) 4305 - 4328, 2018. https://doi.org/10.2140/agt.2018.18.4305