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

Andersen, Kasper LU ; 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.
Please use this url to cite or link to this publication:
author
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
2013-04-09 16:09:50
date last changed
2017-01-01 04:54:40
@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},
  volume       = {157},
  year         = {2004},
}