Yang-Mills theory and Tamagawa numbers
Algebraic Geometry
2014-02-26 v1
Abstract
Atiyah and Bott used equivariant Morse theory applied to the Yang-Mills functional to calculate the Betti numbers of moduli spaces of vector bundles over a Riemann surface, rederiving inductive formulae obtained from an arithmetic approach which involved the Tamagawa number of SL_n. This article surveys this link between Yang-Mills theory and Tamagawa numbers, and explains how methods used over the last three decades to study the singular cohomology of moduli spaces of bundles on a smooth complex projective curve can be adapted to the setting of A^1-homotopy theory to study the motivic cohomology of these moduli spaces.
Cite
@article{arxiv.0801.4733,
title = {Yang-Mills theory and Tamagawa numbers},
author = {Aravind Asok and Brent Doran and Frances Kirwan},
journal= {arXiv preprint arXiv:0801.4733},
year = {2014}
}
Comments
Accepted for publication in the Bulletin of the London Mathematical Society