Virtual Seminar on
Geometry and Topology
https://visgat.cayley.kr
How to join
Zoom Meeting ID 739-035-2844
Password Zero minus the Euler characteristic of a closed oriented surface of genus 4000
Time Wed 4 pm or Thursday 9 am (or so) in KST (Korea Standard Time)
2021
February 3 (W), 2021
10:00am - 11:30pm in Korean time
Inhyeok Choi (KAIST)
Simple length spectra of a generic hyperbolic surface determine its isometry class
Gel'fand asked in 1962 to which extent a closed hyperbolic surface is determined by its length spectrum. Strikingly, the examples of Vignéras and Sunada show that not all surfaces are determined by their length spectra. However, Wolpert proved that 'generic' closed hyperbolic surfaces are determined. Meanwhile, the analogous question with the simple length spectra has not been answered so far. Motivated by the technique of McShane and Parlier, we prove a variant of Wolpert's theorem involving the simple length spectra. To achieve this, we observe a rigidity of length identities over the Teichmüller space, which reads off subsurfaces of low complexity. In this talk, we explain this rigidity and discuss why our argument also applies to infinite-type surfaces. This is joint work with Hyungryul Baik and Dongryul M. Kim.