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

par Ingrid Irmer (SUSTech & IHES)

lundi 10 févr. 2025, 14:00 → 15:15 Europe/Paris

Amphithéâtre Léon Motchane (IHES)

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.