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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 \Sigma. We prove that all intersection numbers in the compactly supported cohomology of M vanish, i.e. "there are no topological L 2 harmonic forms on M". This result generalizes the well known vanishing of the Euler characteristic of the moduli space of... (Update)
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BibTeX entry: (Update)
T. Hausel, Vanishing of intersection numbers on the moduli space of Higgs bundles, Adv. Theor. Math. Phys. 2 (1998) 1011-1040. http://citeseer.ist.psu.edu/hausel98vanishing.html More
@misc{ hausel98vanishing,
author = "T. Hausel",
title = "Vanishing of intersection numbers on the moduli space of Higgs bundles",
text = "T. Hausel, Vanishing of intersection numbers on the moduli space of Higgs
bundles, Adv. Theor. Math. Phys. 2 (1998) 1011-1040.",
year = "1998",
url = "citeseer.ist.psu.edu/hausel98vanishing.html" }
Citations (may not include all citations):162 Principles of algebraic geometry (context) - Griffiths, Harris - 1978
37 The self-duality equations on a Riemann surface (context) - Hitchin - 1987
37 Hyper-Kahler metrics and supersymmetry (context) - Hitchin, Karlhede et al. - 1987
32 Yang-Mills equations over Riemann surfaces (context) - Atiyah, Bott - 1982
26 The geometry and dynamics of magnetic monopoles (context) - Atiyah, Hitchin - 1987
24 Introduction to moduli problems and orbit spaces (context) - Newstead - 1978
21 Stable and unitary vector bundles on a compact Riemann surfa.. (context) - Narasimhan, Seshadri - 1965
15 Higgs bundles and local systems (context) - Simpson - 1992
14 linear systems and the Verlinde formula (context) - Thaddeus - 1994
10 Moduli space of semistable pairs on a curve (context) - Nitsure - 1991
9 The geometry of moduli spaces of sheaves (context) - Huybrechts, Lehn - 1997
7 the cohomology ring of the moduli space of rank 2 vector bun.. (context) - King, Newstead - 1998
7 the cohomology groups of moduli spaces of vector bundles ove.. (context) - Harder, Narasimhan
6 Compactification of moduli of Higgs bundles - Hausel - 1998
5 Groupe Picard des vari'et'es de modules de fibr'es semistabl.. (context) - Drezet, Narasimhan - 1989
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