Yang-Mills theory and Tamagawa numbers: the fascination of unexpected links in mathematics |
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Authors: | Asok Aravind; Doran Brent; Kirwan Frances |
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Institution: | Department of Mathematics University of Washington Box 354250 Seattle, WA 48195 USA asok@math.washington.edu |
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Abstract: | Atiyah and Bott used equivariant Morse theory applied to theYang–Mills functional to calculate the Betti numbers ofmoduli spaces of vector bundles over a Riemann surface, rederivinginductive formulae obtained from an arithmetic approach whichinvolved the Tamagawa number of SLn. This article attempts tosurvey and extend our understanding of this link between Yang–Millstheory and Tamagawa numbers, and to explain how methods usedover the last three decades to study the singular cohomologyof moduli spaces of bundles on a smooth projective curve over can be adapted to the setting of 1-homotopy theory to studythe motivic cohomology of these moduli spaces over an algebraicallyclosed field. |
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