Loops and their complement in a surface
Organizers
Speaker
Xuezhi Zhao
Time
Tuesday, June 24, 2025 3:00 PM - 4:00 PM
Venue
A3-4-301
Online
Zoom 482 240 1589
(BIMSA)
Abstract
The geometric intersection number of two loops on a surface is defined to be the minimal number of intersections of two loops which are respectively homotopic given two loops. Given a set of loop classes, we shall show that the geometric intersection numbers of all pairs of loop classes can be simultaneously realized. In this situation, the complement of these loops in the surface contains some polygons. We shall explain a method to estimate the number of polygons lying in the complements of these loops in the surface.