Dynamics in the moduli space of Abelian differentials.
Avila, Artur, Viana, Marcelo (2005)
Portugaliae Mathematica. Nova Série
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Displaying similar documents to “The Teichmüller geodesic flow and the geometry of the Hodge bundle”
Dynamics in the moduli space of Abelian differentials.
Geodesic reduction via frame bundle geometry.
Bhand, Ajit (2010)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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The associated map of the nonabelian Gauss-Manin connection
Ting Chen (2012)
Open Mathematics
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The Gauss-Manin connection for nonabelian cohomology spaces is the isomonodromy flow. We write down explicitly the vector fields of the isomonodromy flow and calculate its induced vector fields on the associated graded space of the nonabelian Hogde filtration. The result turns out to be intimately related to the quadratic part of the Hitchin map.
The metric in gauge theory: an introduction and some applications
David Groisser (1997)
Banach Center Publications
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We discuss the geometry of the Yang-Mills configuration spaces and moduli spaces with respect to the metric. We also consider an application to a de Rham-theoretic version of Donaldson’s μ-map.
Schottky uniformizations of Z actions on Riemann surfaces.
Rubén A. Hidalgo (2005)
Revista Matemática Complutense
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Given a closed Riemann surface S together a group of its conformal automorphisms H ≅ Z , it is known that there are Schottky uniformizations of S realizing H. In this note we proceed to give an explicit Schottky uniformizations for each of all different topological actions of Z as group of conformal automorphisms on a closed Riemann surface.
Finiteness results for Teichmüller curves
Martin Möller (2008)
Annales de l’institut Fourier
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We show that for each genus there are only finitely many algebraically primitive Teichmüller curves , such that (i) lies in the hyperelliptic locus and (ii) is generated by an abelian differential with two zeros of order . We prove moreover that for these Teichmüller curves the trace field of the affine group is not only totally real but cyclotomic.
Determinant bundle over the universal moduli space of vector bundles over the Teichmüller space
Indranil Biswas (1997)
Annales de l'institut Fourier
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The moduli space of stable vector bundles over a moving curve is constructed, and on this a generalized Weil-Petersson form is constructed. Using the local Riemann-Roch formula of Bismut-Gillet-Soulé it is shown that the generalized Weil-Petersson form is the curvature of the determinant line bundle, equipped with the Quillen metric, for a vector bundle on the fiber product of the universal moduli space with the universal curve.
Topological equivalence of metrics in Teichmüller space.
Liu, Lixin, Sun, Zongliang, Wei, Hanbai (2008)
Annales Academiae Scientiarum Fennicae. Mathematica
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