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

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dc.creatorHausel, Tamas
dc.creatorThaddeus, Michael
dc.date2000-03-16
dc.date2002-07-09
dc.date.accessioned2026-07-07T04:34:19Z
dc.date.available2026-07-07T04:34:19Z
dc.descriptionThe moduli space of stable bundles of rank 2 and degree 1 on a Riemann surface has rational cohomology generated by the so-called universal classes. The work of Baranovsky, King-Newstead, Siebert-Tian and Zagier provided a complete set of relations between these classes, expressed in terms of a recursion in the genus. This paper accomplishes the same thing for the non-compact moduli spaces of Higgs bundles, in the sense of Hitchin and Simpson. There are many more independent relations than for stable bundles, but in a sense the answer is simpler, since the formulas are completely explicit, not recursive. The results of Kirwan on equivariant cohomology for holomorphic circle actions are of key importance. Together, Parts I and II describe the cohomology rings of spaces of rank 2 Higgs bundles at essentially the same level of detail as is known for stable bundles.
dc.description31 pages, LaTeX. Changes in title and introduction only
dc.identifierhttps://arxiv.org/abs/math/0003094
dc.identifierhttp://arxiv.org/abs/math/0003094
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58859
dc.subjectAlgebraic Geometry
dc.subjectMathematical Physics
dc.subjectDifferential Geometry
dc.subjectSymplectic Geometry
dc.subject14H60 (Primary) 14D20, 14H81, 32Q55, 58D27 (Secondary)
dc.titleRelations in the cohomology ring of the moduli space of rank 2 Higgs bundles
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