Sequences of Hitchin representations of Tree-type

Giuseppe Martone

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arXiv · 1910.13585

Sequences of Hitchin representations of Tree-type

Giuseppe Martone

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Abstract

The Hitchin component is a connected component of the character variety of reductive group homomorphisms from the fundamental group of a closed surface S of genus greater than 1 to the Lie group PSL_m(R). The Teichmuller space of S naturally embeds into the Hitchin component. The limit points in the Thurston compactification of the Teichmuller space are well-understood. Our main goal is to provide non-trivial sufficient conditions on a sequence of Hitchin representations so that the limit of this sequence in the Parreau boundary can be described as an action on a tree. These non-trivial conditions are given in terms of Fock-Goncharov coordinates on moduli spaces of generic tuples of flags.

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Giuseppe Martone. 2019-10-29. Sequences of Hitchin representations of Tree-type. https://arxiv.org/abs/1910.13585

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