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

Andersen, Kasper LU orcid ; Bauer, Tilman ; Grodal, Jesper and Pedersen, Erik Kjær (2004) In Inventiones Mathematicae 157(1). p.1-10
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.
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author
; ; and
publishing date
type
Contribution to journal
publication status
published
subject
in
Inventiones Mathematicae
volume
157
issue
1
pages
1 - 10
publisher
Springer
external identifiers
  • scopus:3142657977
ISSN
1432-1297
DOI
10.1007/s00222-003-0341-4
language
English
LU publication?
no
id
e0238ccf-3c34-46b9-b1b2-b779dad83d78 (old id 3412540)
date added to LUP
2016-04-01 12:10:35
date last changed
2022-01-26 23:53:05
@article{e0238ccf-3c34-46b9-b1b2-b779dad83d78,
  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.}},
  author       = {{Andersen, Kasper and Bauer, Tilman and Grodal, Jesper and Pedersen, Erik Kjær}},
  issn         = {{1432-1297}},
  language     = {{eng}},
  number       = {{1}},
  pages        = {{1--10}},
  publisher    = {{Springer}},
  series       = {{Inventiones Mathematicae}},
  title        = {{A finite loop space not rationally equivalent to a compact Lie group}},
  url          = {{http://dx.doi.org/10.1007/s00222-003-0341-4}},
  doi          = {{10.1007/s00222-003-0341-4}},
  volume       = {{157}},
  year         = {{2004}},
}