On the pullback relation on curves induced by a Thurston map

Abstract

Via taking connected components of preimages, a Thurston map $f:(S^2,P_f)\to (S^2,P_f)$ induces a pullback relation on the set of isotopy classes of curves in the complement of its postcritical set $P_f$. We survey known results about the dynamics of this relation, and pose some questions.

12 pages, 1 figure