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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Rational homotopy of gauge groups


Authors: Yves Félix and John Oprea
Journal: Proc. Amer. Math. Soc. 137 (2009), 1519-1527
MSC (2000): Primary 55P99; Secondary 57R91, 57S05
Published electronically: November 20, 2008
MathSciNet review: 2465678
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Abstract: In this brief paper, we observe that basic results from rational homotopy theory provide formulas for the rational homotopy groups of gauge groups of principal bundles $ K \to P \to B$ in terms of the rational homotopy groups of $ K$ and cohomology groups of $ B$ alone.


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Additional Information

Yves Félix
Affiliation: Institut de Mathématique Pure et Appliquée, Chemin du Cyclotron, 2, B-1348Louvain-la-Neuve, Belgium
Email: Yves.Felix@uclouvain.be

John Oprea
Affiliation: Department of Mathematics, Cleveland State University, Cleveland, Ohio 44115
Email: j.oprea@csuohio.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09721-9
PII: S 0002-9939(08)09721-9
Keywords: Gauge group, mapping space, principal bundle
Received by editor(s): July 1, 2008
Received by editor(s) in revised form: August 4, 2008
Published electronically: November 20, 2008
Communicated by: Paul Goerss
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.