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

 

On the Yang-Mills stratification for surfaces


Author: Daniel A. Ramras
Journal: Proc. Amer. Math. Soc. 139 (2011), 1851-1863
MSC (2010): Primary 53C07, 58D27; Secondary 58E15, 05A20
Published electronically: October 20, 2010
MathSciNet review: 2763772
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Abstract: Atiyah and Bott showed that Morse theory for the Yang-Mills functional can be used to study the space of flat, or more generally central, connections on a bundle over a Riemann surface. These methods have recently been extended to non-orientable surfaces by Ho and Liu. In this article, we use Morse theory to determine the exact connectivity of the natural map from the homotopy orbits of the space of central Yang-Mills connections to the classifying space of the gauge group. The key ingredient in this computation is a combinatorial study of the Morse indices of Yang-Mills critical sets.


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Additional Information

Daniel A. Ramras
Affiliation: Department of Mathematical Sciences, New Mexico State University, P.O. Box 30001, Department 3MB, Las Cruces, New Mexico 88003-8001

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10614-7
PII: S 0002-9939(2010)10614-7
Received by editor(s): January 13, 2010
Received by editor(s) in revised form: May 24, 2010
Published electronically: October 20, 2010
Additional Notes: This work was partially supported by NSF grants DMS-0353640 (RTG), DMS-0804553, and DMS-0968766
Communicated by: Richard A. Wentworth
Article copyright: © Copyright 2010 Daniel A. Ramras