Affiliation:
1. University of Hawaii at Manoa, Keller, Honolulu, HI, USA
Abstract
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 study intersection numbers of curves contained in geodesics in the curve graph. Furthermore, we generalize a well-known result on intersection number growth of curves under iteration of Dehn twists and multitwists for all kinds of pure mapping classes.
Funder
U.S. National Science Foundation
GEAR Network
Publisher
Oxford University Press (OUP)
Reference13 articles.
1. Determining the finite subgraphs of curve graphs;Aougab;Groups Geom. Dyn.
2. Asymptotic geometry of the mapping class group and Teichmüller space;Behrstock;Geom. Topol.,2006
3. Comparison between Teichmüller and Lipschitz metrics;Choi;J. Lond. Math. Soc. (2),2007
4. Minimal pseudo-Anosov translation lengths on the complex of curves;Gadre;Geom. Topol.,2011
5. Coloring curves on surfaces;Gaster,2018