Distances and intersections of curves

TL;DR

This paper establishes a relationship between intersection numbers of curves and their subsurface projection distances, providing new insights and applications in the study of curve graphs and mapping class groups.

Contribution

It introduces a coarse relationship with explicit quasi-constants linking intersection numbers and projection distances, advancing understanding in geometric topology.

Findings

Relationship between intersection numbers and projection distances with explicit bounds

Applications to curve graphs and mapping class groups

Enhanced tools for geometric analysis of curves

Abstract

We obtain a coarse relationship between geometric intersection numbers of curves and the sum of their subsurface projection distances with explicit quasi-constants. By using this relationship, we give applications in the studies of the curve graphs and the mapping class groups.