Quasi finite loop spaces are manifolds

N. Kitchloo; D. Notbohm

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arXiv · math/0209103

Quasi finite loop spaces are manifolds

N. Kitchloo·D. Notbohm

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Abstract

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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BibTeX RIS

N. Kitchloo, D. Notbohm. 2002-09-10. Quasi finite loop spaces are manifolds. https://arxiv.org/abs/math/0209103

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