---
_id: '1450'
abstract:
- lang: eng
text: 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.
acknowledgement: "First of all I would like to thank my supervisor Nigel Hitchin for
suggesting Problem 1, and for his help and \r\n encouragement. I am grateful to
Michael Thaddeus for his inspiring paper [Thai], enlightening communications and
his constant interest in my work. I am also indebted to Manfred Lehn for the idea
of the proof of Theorem 6.2. I have found\r\nconversations with Michael Atiyah,
Frances Kirwan and Graeme Segal very stimulating. I thank the Mathematical Institute
and St. Catherine's College, Oxford for their hospitality during the preparation
of this work. Finally I thank Trinity College, Cambridge for financial support."
article_processing_charge: No
article_type: original
author:
- first_name: Tamas
full_name: Hausel, Tamas
id: 4A0666D8-F248-11E8-B48F-1D18A9856A87
last_name: Hausel
citation:
ama: 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
apa: Hausel, 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.a3
chicago: Hausel, 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.
ieee: 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.
ista: Hausel T. 1998. Vanishing of intersection numbers on the moduli space of Higgs
bundles. Advances in Theoretical and Mathematical Physics. 2(5), 1011–1040.
mla: 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.
short: T. Hausel, Advances in Theoretical and Mathematical Physics 2 (1998) 1011–1040.
date_created: 2018-12-11T11:52:06Z
date_published: 1998-09-01T00:00:00Z
date_updated: 2022-09-01T14:09:49Z
day: '01'
doi: 10.4310/ATMP.1998.v2.n5.a3
extern: '1'
external_id:
arxiv:
- math/9805071
intvolume: ' 2'
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/math/9805071
month: '09'
oa: 1
oa_version: Preprint
page: 1011 - 1040
publication: Advances in Theoretical and Mathematical Physics
publication_identifier:
issn:
- 1095-0761
publication_status: published
publisher: International Press
publist_id: '5747'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Vanishing of intersection numbers on the moduli space of Higgs bundles
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 2
year: '1998'
...