Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
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
MathSciNet review: 3043027
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 53B20, 53C99

Retrieve articles in all journals with MSC (2010): 53B20, 53C99

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
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia