Séminaire Géométrie et groupes discrets

The Thurston Spine and Critical Points of the Systole Function on Teichmüller Space

by Ingrid Irmer (SUSTech & IHES)

Europe/Paris
Amphithéâtre Léon Motchane (IHES)

Amphithéâtre Léon Motchane

IHES

Le Bois Marie 35, route de Chartres CS 40001 91893 Bures-sur-Yvette Cedex
Description

Thurston defined a mapping class group-equivariant spine for Teichmüller space: the "Thurston spine". This spine is a CW complex, consisting of the points in Teichmüller space at which the set of shortest geodesics — the systoles — cut the surface into polygons. The systole function is a map from Teichmüller space to R+ whose value at any point is given by the length of the systoles. It is known that the systole function is a topological Morse function on Teichmüller space, whose critical points are contained in the Thurston spine. This talk surveys what the systole function tells us about the Thurston spine.

Organized by

Fanny Kassel

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