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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the Yang–Mills stratification for surfaces
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by Daniel A. Ramras PDF
Proc. Amer. Math. Soc. 139 (2011), 1851-1863

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
  • 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
  • © Copyright 2010 Daniel A. Ramras
  • Journal: Proc. Amer. Math. Soc. 139 (2011), 1851-1863
  • MSC (2010): Primary 53C07, 58D27; Secondary 58E15, 05A20
  • DOI: https://doi.org/10.1090/S0002-9939-2010-10614-7
  • MathSciNet review: 2763772