Small intersection numbers in the curve graph
Abstract
Let $S_{g,p}$ denote the genus $g$ orientable surface with $p \ge 0$ punctures, and let $\omega(g,p)= 3g+p4$. We prove the existence of infinitely long geodesic rays $\left\{v_{0},v_{1}, v_{2}, ...\right\}$ in the curve graph satisfying the following optimal intersection property: for any natural number $k$, the endpoints $v_{i},v_{i+k}$ of any length $k$ subsegment intersect $O(\omega^{k2})$ times. By combining this with work of the first author, we answer a question of Dan Margalit.
 Publication:

arXiv eprints
 Pub Date:
 October 2013
 arXiv:
 arXiv:1310.4711
 Bibcode:
 2013arXiv1310.4711A
 Keywords:

 Mathematics  Geometric Topology
 EPrint:
 13 pages, 6 figures