Simple Length Rigidity for Hitchin Representations

Martin Bridgeman; Richard Canary; François Labourie

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arXiv · 1703.07336

Simple Length Rigidity for Hitchin Representations

Martin Bridgeman·Richard Canary·François Labourie

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Abstract

We show that a Hitchin representation is determined by the spectral radii of the images of simple, non-separating closed curves. As a consequence, we classify isometries of the intersection function on Hitchin components of dimension 3 and on the self-dual Hitchin components in all dimensions. As an important tool in the proof, we establish a transversality result for positive quadruples of flags.

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Martin Bridgeman, Richard Canary, François Labourie. 2017-03-21. Simple Length Rigidity for Hitchin Representations. https://arxiv.org/abs/1703.07336

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