Quasi finite loop spaces are manifolds

Details Quasi finite loop spaces are manifolds Quasi finite loop spaces are manifolds

2002-09-10

arxiv.org/abs/math/0209103v1

Mathematics

Algebraic Topology

17 pages

Scientific paper

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.

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