Koç Üniversitesi Matematik Bölümü Seminerleri
Curves on surfaces with prescribed intersection numbers
Ferit Öztürk
Boğaziçi University, Türkiye
Given N choose 2 integers, can you find N nontrivial, oriented simple closed curves on a torus such that their pairwise signed intersection numbers are the given integers? I will give a necessary and sufficient condition to realize such a scheme on a torus and discuss about the problem in all genera g >= 0 with and without boundary. I will talk about some consequences relating to low dimensional topology and graph theory.
