Chern-Simons classes and the Ricci flow on 3-manifolds
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- by Christopher Godbout PDF
- Proc. Amer. Math. Soc. 141 (2013), 2467-2474 Request permission
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
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Additional Information
- Christopher Godbout
- Affiliation: Department of Mathematics, Lehigh University, Bethlehem, Pennsylvania 18015-3174
- 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
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 2467-2474
- MSC (2010): Primary 53B20, 53C99
- DOI: https://doi.org/10.1090/S0002-9939-2013-11606-0
- MathSciNet review: 3043027