Simple Length Rigidity for Hitchin Representations

Martin Bridgeman (1) , Richard Canary (2) , François Labourie (3)

1 BC - Boston College
2 Department of Mathematics - University of Michigan
3 LJAD - Laboratoire Jean Alexandre Dieudonné

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.

Domaines: Géométrie différentielle [math.DG]

Martin Bridgeman, Richard Canary, François Labourie. Simple Length Rigidity for Hitchin Representations. Advances in Mathematics, 2020, ⟨10.1016/j.aim.2019.106901⟩. ⟨hal-01654568⟩