Séminaire GT3
organisé par l'équipe Géométrie
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Sylvain Douteau
Intersection cohomology is a stratified cohomology theory
13 janvier 2025 - 14:00Salle de séminaires IRMA
Objects with singularities are ubiquitous when dealing with manifolds, but are usually tame objects: Pseudo-manifolds which can be equipped with suitable stratifications (à la Whitney or Thom-Mather).
In the 1980, Goresky and MacPherson introduced intersection cohomology. A new invariant, which extends ordinary cohomology and gives pseudo-manifolds the cohomological properties expected of manifolds such as Poincaré duality.
However, by construction, intersection cohomology is not a cohomology theory in the usual sense. It has been an open problem since its introduction to find a context in which intersection cohomology can be interpreted as an actual cohomology theory.
In this talk, I will present such a context inspired by the A^1-homotopy theory of Morel and Voevodsky. This is based on work in progress, joint with David Chataur. -
Stavros Garoufalidis
TBA
20 janvier 2025 - 11:00Salle de conférences IRMA
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Ingrid Irmer
The Thurston spine and critical points of the systole function on Teichmüller space
20 janvier 2025 - 14:00Salle de séminaires IRMA
Abstract - 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 $\mathbb{R}_{+}$ 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 TeichmÛller space, whose critical points are contained in the Thurston spine. This talk surveys what the systole function tells us about the Thurston spine.