Vanishing of intersection numbers on the moduli space of Higgs bundles

T. Hausel, Advances in Theoretical and Mathematical Physics 2 (1998) 1011–1040.


Journal Article | Published
Abstract
In this paper we consider the topological side of a problem which is the analogue of Sen's S-duality testing conjecture for Hitchin's moduli space M of rank 2 stable Higgs bundles of fixed determinant of odd degree over a Riemann surface ∑. We prove that all intersection numbers in the compactly supported cohomology of M vanish, i.e. "there are no topological L2 harmonic forms on M". This result generalizes the well known vanishing of the Euler characteristic of the moduli space of rank 2 stable bundles N of fixed determinant of odd degree over ∑. Our proof shows that the vanishing of all intersection numbers of H* cpt(M) is given by relations analogous to the Mumford relations in the cohomology ring of N.
Publishing Year
Date Published
1998-09-01
Journal Title
Advances in Theoretical and Mathematical Physics
Volume
2
Issue
5
Page
1011 - 1040
IST-REx-ID

Cite this

Hausel T. Vanishing of intersection numbers on the moduli space of Higgs bundles. Advances in Theoretical and Mathematical Physics. 1998;2(5):1011-1040. doi:10.4310/ATMP.1998.v2.n5.a3
Hausel, T. (1998). Vanishing of intersection numbers on the moduli space of Higgs bundles. Advances in Theoretical and Mathematical Physics, 2(5), 1011–1040. https://doi.org/10.4310/ATMP.1998.v2.n5.a3
Hausel, Tamas. “Vanishing of Intersection Numbers on the Moduli Space of Higgs Bundles.” Advances in Theoretical and Mathematical Physics 2, no. 5 (1998): 1011–40. https://doi.org/10.4310/ATMP.1998.v2.n5.a3.
T. Hausel, “Vanishing of intersection numbers on the moduli space of Higgs bundles,” Advances in Theoretical and Mathematical Physics, vol. 2, no. 5, pp. 1011–1040, 1998.
Hausel T. 1998. Vanishing of intersection numbers on the moduli space of Higgs bundles. Advances in Theoretical and Mathematical Physics. 2(5), 1011–1040.
Hausel, Tamas. “Vanishing of Intersection Numbers on the Moduli Space of Higgs Bundles.” Advances in Theoretical and Mathematical Physics, vol. 2, no. 5, International Press, 1998, pp. 1011–40, doi:10.4310/ATMP.1998.v2.n5.a3.

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