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

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Author

Summary, in English

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.

Publishing year

2004

Language

English

Pages

1-10

Publication/Series

Inventiones Mathematicae

Volume

157

Issue

1

Document type

Journal article

Publisher

Springer

Topic

  • Mathematics

Status

Published

ISBN/ISSN/Other

  • ISSN: 1432-1297