article
Vanishing of intersection numbers on the moduli space of Higgs bundles
published
Tamas
Hausel
author 4A0666D8-F248-11E8-B48F-1D18A9856A87
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.
International Press1998
Advances in Theoretical and Mathematical Physics10.4310/ATMP.1998.v2.n5.a3
251011 - 1040
yes
Hausel, Tamas. “Vanishing of Intersection Numbers on the Moduli Space of Higgs Bundles.” <i>Advances in Theoretical and Mathematical Physics</i> 2, no. 5 (1998): 1011–40. <a href="https://doi.org/10.4310/ATMP.1998.v2.n5.a3">https://doi.org/10.4310/ATMP.1998.v2.n5.a3</a>.
Hausel, T. (1998). Vanishing of intersection numbers on the moduli space of Higgs bundles. <i>Advances in Theoretical and Mathematical Physics</i>, <i>2</i>(5), 1011–1040. <a href="https://doi.org/10.4310/ATMP.1998.v2.n5.a3">https://doi.org/10.4310/ATMP.1998.v2.n5.a3</a>
T. Hausel, “Vanishing of intersection numbers on the moduli space of Higgs bundles,” <i>Advances in Theoretical and Mathematical Physics</i>, 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.” <i>Advances in Theoretical and Mathematical Physics</i>, vol. 2, no. 5, International Press, 1998, pp. 1011–40, doi:<a href="https://doi.org/10.4310/ATMP.1998.v2.n5.a3">10.4310/ATMP.1998.v2.n5.a3</a>.
T. Hausel, Advances in Theoretical and Mathematical Physics 2 (1998) 1011–1040.
Hausel T. Vanishing of intersection numbers on the moduli space of Higgs bundles. <i>Advances in Theoretical and Mathematical Physics</i>. 1998;2(5):1011-1040. doi:<a href="https://doi.org/10.4310/ATMP.1998.v2.n5.a3">10.4310/ATMP.1998.v2.n5.a3</a>
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