Intersection numbers in the curve graph with a uniform constant

Abstract

We derive various inequalities involving the intersection number of the curves contained in geodesics and tight geodesics in the curve graph. While there already exist such inequalities on tight geodesics, our method applies in the setting of geodesics. Furthermore, the method gives inequalities with a uniform constant depending only on the topology of the surface.

Minor revisions following comments from the referees

References in corpus (1)

• Uniform local finiteness of the curve graph via subsurface projections

Cited by in corpus (1)

• Efficient geodesics and an effective algorithm for distance in the complex of curves