A finite loop space not rationally equivalent to a compact Lie group

Abstract

We construct a connected finite loop space of rank $66$ and dimension $1254$ whose rational cohomology is not isomorphic as a graded vector space to the rational cohomology of any compact Lie group, hence providing a counterexample to a classical conjecture. Aided by machine calculation we verify that our counterexample is minimal, i.e., that any finite loop space of rank less than $66$ is in fact rationally equivalent to a compact Lie group, extending the classical known bound of $5$.

Publication
Inventiones Mathematicae 157/1 (2004), pp. 1–10
Date
Links
PDF