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

 

Chern-Simons classes and the Ricci flow on 3-manifolds


Author: Christopher Godbout
Journal: Proc. Amer. Math. Soc. 141 (2013), 2467-2474
MSC (2010): Primary 53B20, 53C99
Published electronically: February 14, 2013
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Abstract: In 1974, S.-S. Chern and J. Simons published a paper where they defined a new type of characteristic class, one that depends not just on the topology of a manifold but also on the geometry. The goal of this paper is to investigate what kinds of geometric information is contained in these classes by studying their behavior under the Ricci flow. In particular, it is shown that the Chern-Simons class corresponding to the first Pontryagin class is invariant under the Ricci flow on the warped products $ S^2\times _f S^1$ and $ S^1 \times _f S^2$ but that this class is not invariant under the Ricci flow on a generalized Berger sphere.


References [Enhancements On Off] (What's this?)

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Additional Information

Christopher Godbout
Affiliation: Department of Mathematics, Lehigh University, Bethlehem, Pennsylvania 18015-3174

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11606-0
PII: S 0002-9939(2013)11606-0
Received by editor(s): November 15, 2010
Received by editor(s) in revised form: October 4, 2011, and October 8, 2011
Published electronically: February 14, 2013
Additional Notes: This work is part of the author’s dissertation at Lehigh University. The author wishes to thank his advisor, David Johnson, for his help and insight.
Communicated by: Daniel Ruberman
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.