Flows on the PGL(V)-Hitchin component

Abstract:

In this article we define new flows on the Hitchin components for \mathrmPGL(V). Special examples of these flows are associated to simple closed curves on the surface and give generalized twist flows. Other examples, so called eruption flows, are associated to pair of pants in S and capture new phenomena which are not present in the case when n = 2. Using these flows, we construct a global coordinate system on the Hitchin component. In a companion paper to this article two of the authors develop new tools to compute the Goldman symplectic form on the Hitchin component, and prove that this global coordinate system is a Darboux coordinate system.

SEEK ID: https://publications.h-its.org/publications/968

Research Groups: Groups and Geometry

Publication type: Misc

Journal: arXiv,math.DG,1709.03580

Citation: arXiv,math.DG,1709.03580

Date Published: 2017

URL: https://arxiv.org/abs/1709.03580

Registered Mode: imported from a bibtex file

Authors: Zhe Sun, Anna Wienhard, Tengren Zhang

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Created: 30th Jan 2020 at 09:49

Last updated: 5th Mar 2024 at 21:24

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