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Variations along the Fuchsian locus

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arxiv 1506.01686 v2 pith:YYFAUTAY submitted 2015-06-04 math.DG

François Labourie , Richard Wentworth This is my paper · ORCID
classification math.DG
keywords alongexpressionfuchsianlocusrelationshipvariationsclassicalcomponent
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The main result is an explicit expression for the Pressure Metric on the Hitchin component of surface group representations into PSL(n,R) along the Fuchsian locus. The expression is in terms of a parametrization of the tangent space by holomorphic differentials, and it gives a precise relationship with the Petersson pairing. Along the way, variational formulas are established that generalize results from classical Teichmueller theory, such as Gardiner's formula, the relationship between length functions and Fenchel-Nielsen deformations, and variations of cross ratios.

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  1. Non-Abelian Hodge Theory and Related Topics

    math.AG 2019-08 conditional novelty 4.0 of 10

    A survey of non-Abelian Hodge theory and related moduli spaces, with a new explicit description of Simpson filtrations for rank 3 flat bundles.

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