Spaces of geodesic triangulations of surfaces

Speaker: Yanwen Luo, SFU

Date: Wed, Nov 29, 2023

Location: Online

Conference: Emergent Research: The PIMS Postdoctoral Fellow Seminar

Subject: Mathematics

Class: Scientific


In 1962, Tutte proposed a simple method to produce a straight-line embedding of a planar graph in the plane, known as Tutte's spring theorem. It leads to a surprisingly simple proof of a classical theorem proved by Bloch, Connelly, and Henderson in 1984, which states that the space of geodesic triangulations of a convex polygon is contractible. In this talk, I will introduce spaces of geodesic triangulations of surfaces, review Tutte's spring theorem, and present this short proof. It time permits, I will briefly report the recent progress in identifying the homotopy types of spaces of geodesic triangulations of general surfaces.