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

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

2003-06-16

arxiv.org/abs/math/0306234v1

Invent. Math 157 (2004), no. 1, 1--10.

Mathematics

Algebraic Topology

8 pages

Scientific paper

10.1007/s00222-003-0341-4

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.

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