Intersection number and systole on hyperbolic surfaces

2022-04-28 15:33 - 17:33

Abstract: Let X be a compact hyperbolic surface. We can see that there is a constant C(X) such that the intersection number of the closed geodesics is  \leq C(X) times the product of their lengths. Consider the optimum constant C(X). In this talk, we describe its asymptotic behavior in terms of systole,  length of the shortest closed geodesic on X.