Teichmüller Space is Distorted in the Hitchin Component

par Pierre-Louis Blayac (University of Michigan)

lundi 8 janv. 2024, 16:00 → 17:15 Europe/Paris

Amphithéâtre Léon Motchane (IHES)

Given a closed topological surface S of genus at least two and an integer d, the Teichmüller space of S embeds into the space of conjugacy classes of representations of the fundamental group of S to PSL(d,R) by postcomposing by the irreducible representation from PSL(2,R) to PSL(d,R). The connected component of the Teichmüller space in this space is called the Hitchin component.

A few years ago, Bridgeman, Canary, Labourie and Sambarino constructed on this component several metrics called pressure metrics. The construction is inspired by a characterization of the Weil-Petersson metric due to Thurston and Wolpert, and work of McMullen. These metrics are not yet fully understood. We will describe their restriction to a subspace of the Hitchin component consisting of deformations by bending of points of the Teichmüller space. This will allow us to show that the Teichmüller is distorted, in the sense that there is a sequence of points in the Teichmüller space whose Weil-Petersson distance to the origin diverges while their pressure