Computing the fractional Dehn twist coefficient of braids using non-crossing partition diagrams

Series
Geometry Topology Seminar
Time
Monday, October 12, 2026 - 2:00pm for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Organizer
John Etnyre

The dual Garside left canonical form is used to solve the conjugacy problem in braid theory, introduced by Xu (3-braids), Kang-Ko-Lee (4-braids) and Birman-Ko-Lee (n-braids). The fractional Dehn twist coefficient (FDTC) is a measurement of the boundary twist of a surface homeomorphism, introduced by Honda-Kazez-Matic. In contact geometry, it is a powerful tool to detect tightness/overtwistedness of a given contact structure. In this talk, I will give applications of the left canonical form to the computation of the FDTC of 4-braids.