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Topology/Geometry Seminar

The space of geodesic triangulations on surfaces

Yanwen Luo (Rutgers)

Location:  zoom link: https://rutgers.zoom.us/j/96839448491?pwd=NHNWcVFKTWpkRDZWcVVhVm9mYTNGUT09
Date & time: Tuesday, 15 September 2020 at 3:50PM - 4:50PM

In 1959, Smale showed that the group of diffeomorphisms of the closed 2-disk which are identity on the boundary is a contractible space. In 1984, Bloch, Connelly, and Henderson proved the discrete version of this theorem: the space of simplexwise linear homeomorphisms of a convex polygon is contractible.

In this talk, we will show that the idea in Tutte's Embedding Theorem can be applied to give a simplified proof of the Bloch-Connelly-Henderson theorem. We will also discuss the homotopy types of the corresponding spaces when the boundary polygon is not convex. Finally, we will discuss the conjecture about the topology of the spaces of geodesic triangulations on closed surfaces.