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

@article{Hausel1998VanishingOI, title={Vanishing of intersection numbers on the moduli space of Higgs bundles}, author={Tam{\'a}s Hausel}, journal={arXiv: Algebraic Geometry}, year={1998} }

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 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 vanish, i.e. "there are no topological L^2 harmonic forms on Hitchin's space". This result generalizes the well known vanishing of the Euler characteristic of the moduli space of rank 2… Expand

#### 38 Citations

Generators for the cohomology ring of the moduli space of rank 2 Higgs bundles

- Mathematics, Physics
- 2000

The moduli space of stable vector bundles on a Riemann surface is smooth when the rank and degree are coprime, and is diffeomorphic to the space of unitary connections of central constant curvature.… Expand

Geometry of the moduli space of Higgs bundles

- Physics, Mathematics
- 1998

This thesis contains work which appeared in several papers. Additionally to the results in the papers it contains a detailed introduction and some further proofs and remarks. The dissertation gives a… Expand

On the cohomology ring of the moduli space of Higgs bundles II: Relations in rank 2

- Mathematics
- 2000

This is a continuation of Part I of the paper of the same name. The Higgs bundles in question are pairs consisting of a holomorphic vector bundle E on a complex projective curve C , together with a… Expand

The asymptotic geometry of the Higgs bundle moduli space over a Riemann surface

- 2015

The moduli space of Higgs bundles, introduced by Hitchin [5] and Simpson [10], is a well investigated object in algebraic geometry and topology. In our talk we discussed our recent results in [7, 8]… Expand

On the cohomology ring of the moduli space of Higgs bundles I: Generators of the ring

- Physics
- 2000

A central object of study in gauge theory is the moduli space of unitary flat connections on a compact surface. Thanks to the efforts of many people, a great deal is understood about the ring… Expand

Relations in the cohomology ring of the moduli space of rank 2 Higgs bundles

- Mathematics, Physics
- 2000

paper is to characterize the rational cohomology ring of 7-n when the rank is 2 and the degree is odd. In fact, we have given a complete set of generators for this ring in another paper [14]. So it… Expand

Ends of the moduli space of Higgs bundles

- Mathematics
- 2016

We associate to each stable Higgs pair (A(0), Phi(0)) on a compact Riemann surface X a singular limiting configuration (A(infinity), Phi(infinity)), assuming that det Phi has only simple zeroes. We… Expand

The intersection form on moduli spaces of twisted PGL_n-Higgs bundles vanishes

- Mathematics
- 2014

Hausel and Rodriguez-Villegas conjectured that the intersection form on the moduli space of stable PGL_n-Higgs bundles on a curve vanishes if the degree is coprime to n. In this note we prove this… Expand

Global topology of the Hitchin system

- Mathematics
- 2011

Here we survey several results and conjectures on the cohomology of the total space of the Hitchin system: the moduli space of semi-stable rank n and degree d Higgs bundles on a complex algebraic… Expand

The intersection form on moduli spaces of twisted $$PGL_n$$PGLn-Higgs bundles vanishes

- Mathematics
- 2016

Hausel and Rodriguez-Villegas conjectured that the intersection form on the moduli space of stable $$\textsf {PGL}_n$$PGLn-Higgs bundles on a curve vanishes if the degree is coprime to n. In this… Expand

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