MATHEMATICS SEMINAR by Ferit Öztürk

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.