A finite loop space not rationally equivalent to a compact Lie group
(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:
https://lup.lub.lu.se/record/3412540
- author
- Andersen, Kasper LU ; Bauer, Tilman ; Grodal, Jesper and Pedersen, Erik Kjær
- publishing date
- 2004
- 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}}, }