Geodesic
The index formula for the moduli of $G$-bundles on a curve
Constantin Teleman1 ; Christopher T. Woodward2
1Department of Mathematics<br/>University of California<br/>970 Evans Hall #3840<br/>Berkeley, CA 94720-3840<br/>United States
2Department of Mathematics<br/>Rutgers University<br/>110 Frelinghuysen Rd.<br/>Piscataway, NJ 08854-8019<br/>United States
Annals of mathematics, Tome 170 (2009) no. 2, pp. 495-527
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We prove the formulae conjectured by the first author for the index of $K$-theory classes over the moduli stack of algebraic $G$-bundles on a smooth projective curve. The formulae generalize E. Verlinde’s for line bundles and have Witten’s integrals over the moduli space of stable bundles as their large level limits. As an application, we prove the Newstead-Ramanan conjecture on the vanishing of high Chern classes of certain moduli spaces of semi-stable $G$-bundles.

DOI : 10.4007/annals.2009.170.495

Constantin Teleman  1   ; Christopher T. Woodward  2

1 Department of Mathematics<br/>University of California<br/>970 Evans Hall #3840<br/>Berkeley, CA 94720-3840<br/>United States
2 Department of Mathematics<br/>Rutgers University<br/>110 Frelinghuysen Rd.<br/>Piscataway, NJ 08854-8019<br/>United States 
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Constantin Teleman; Christopher T. Woodward. The index formula for the moduli of $G$-bundles on a curve. Annals of mathematics, Tome 170 (2009) no. 2, pp. 495-527. doi: 10.4007/annals.2009.170.495

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