Geometry of the moduli space of Higgs bundles

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dc.creatorHausel, Tamas
dc.date2001-07-05
dc.date.accessioned2026-07-07T04:42:30Z
dc.date.available2026-07-07T04:42:30Z
dc.descriptionThis 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 description of the topology and symplectic and algebraic geometry of Hitchin's hyperkaehler moduli space M of rank 2 Higgs bundles with fixed determinant of odd degree over a fixed Riemann surface. After the long introduction it describes a compactification of M in great detail, using symplectic cutting (math.AG/9804083). Examining the downward Morse flow of a natural circle action on M it shows the vanishing of intersection numbers (math.AG/9805071). Examining the upward Morse flow it explains a set of generators of the cohomology ring and a conjectured explicit description of the cohomology ring (which was proven in math.AG/0003094). Then finally it introduces the resolution tower for M, and shows that its direct limit is homotopically equivalent with the classifying space of the gauge group. In turn it yields another proof of the generation theorem (as in math.AG/0003093) and also yields a purely algebraic geometric proof of the Mumford conjecture about the cohomology ring of the moduli space of rank 2 stable bundles on curves. It finishes by proving homotopy stabilizations in the resolution tower analogously to the Atiyah-Jones conjecture.
dc.descriptionauthor's 1998 PhD thesis, 116 pages
dc.identifierhttps://arxiv.org/abs/math/0107040
dc.identifierhttp://arxiv.org/abs/math/0107040
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/61806
dc.subjectAlgebraic Geometry
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.subjectDifferential Geometry
dc.subjectSymplectic Geometry
dc.titleGeometry of the moduli space of Higgs bundles
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