Quasi finite loop spaces are manifolds
Abstract
Description
It is an old conjecture, that finite $H$-spaces are homotopy equivalent to manifolds. Here we prove that this conjecture is true for loop spaces. Actually, we show that every quasi finite loop space is equivalent to a stably parallelizable manifold. The proof is conceptual and relies on the theory of p-compact groups. On the way we also give a complete classification of all simple 2-compact groups of rank 2.
17 pages
17 pages