Resumen de Small intersection numbers in the curve graph

Tarik Aougab, Samuel J. Taylor

• Let S g,p denote the genus g orientable surface with p=0 punctures, and let ?(g,p)=3g+p-3>1 . We prove the existence of infinitely long geodesic rays (v 0 ,v 1 ,v 2 ,�) in the curve graph satisfying the following optimal intersection property: for any natural numbers i and k , the endpoints v i ,v i+k of any length k subsegment intersect at most f i,k (?) times, where f i,k (x) is O(x k-2 ) . This answers a question of Dan Margalit