# Vanishing of intersection numbers on the moduli space of Higgs bundles

Hausel T. 1998. Vanishing of intersection numbers on the moduli space of Higgs bundles. Advances in Theoretical and Mathematical Physics. 2(5), 1011–1040.

Download (ext.)

*Journal Article*|

*Published*

Author

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.a3Hausel, T. (1998). Vanishing of intersection numbers on the moduli space of Higgs bundles.

*Advances in Theoretical and Mathematical Physics*. International Press. https://doi.org/10.4310/ATMP.1998.v2.n5.a3Hausel, Tamás. “Vanishing of Intersection Numbers on the Moduli Space of Higgs Bundles.”

*Advances in Theoretical and Mathematical Physics*. International Press, 1998. 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. International Press, pp. 1011–1040, 1998.Hausel, Tamás. “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.**All files available under the following license(s):**

**Copyright Statement:**

**This Item is protected by copyright and/or related rights.**[...]

**Link(s) to Main File(s)**

Access Level

Open Access