Geometry/Topology Seminar: Contractibility of Teichmüller space, by Chaitanya Tappu
November 20, 2024
3:00 PM - 3:50 PM
Chaitanya Tappu (Cornell University): Contractibility of Teichmüller space
In this talk, I will prove that the marked moduli space of any infinite type surface is contractible. The marked moduli space of an infinite type surface (equipped with an action of the big mapping class group) was introduced in my earlier work, as the generalisation of the usual Teichmüller space of a finite type surface. This result is analogous to that of Douady--Earle, who proved that the (quasiconformal) Teichmüller space of an arbitrary Riemann surface, whether of finite or infinite type, is contractible. Even though the marked moduli space reduces to the Teichmüller space in case the surface is of finite type, it is quite distinct from the Teichmüller space in case the surface is of infinite type. Nevertheless, we are able to adapt the Douady--Earle proof to the setting of the marked moduli space. A key difference is that in this setting, we use a Fréchet space topology on the vector space of (-1, 1)-forms (that is, Beltrami forms), rather than the usual Banach space topology.
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Date posted
Nov 20, 2024
Date updated
Nov 20, 2024
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