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

Andersen, Kasper K. S.; Bauer, Tilman; Grodal, Jesper; Pedersen, Erik K.

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

Authors

Andersen, Kasper K. S.

Bauer, Tilman

Grodal, Jesper

Pedersen, Erik K.

Description

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.
8 pages