Topology Seminar: Patrick Reynolds
Topic
Minimal algebraic laminations and arational trees
Speakers
Details
Abstract:
Associated to a tree T in the boundary of Outer space is a symbolic dynamical system called the dual lamination of T, denoted L^2(T). We develop a two-part inductive procedure for studying L^2(T). One part is known: it is a slight generalization of the Rips machine as developed by Coulbois-Hilion; the other part is new: it is a generalization of the classical Rauzy-Veech induction. As an application we characterize trees T for which L^2(T) is minimal. As a further application we give a description of the Gromov boundary of the complex of free factors: it is the space of measure classes of arational trees. (Jointly with T. Coulbois and A. Hilion.)
Associated to a tree T in the boundary of Outer space is a symbolic dynamical system called the dual lamination of T, denoted L^2(T). We develop a two-part inductive procedure for studying L^2(T). One part is known: it is a slight generalization of the Rips machine as developed by Coulbois-Hilion; the other part is new: it is a generalization of the classical Rauzy-Veech induction. As an application we characterize trees T for which L^2(T) is minimal. As a further application we give a description of the Gromov boundary of the complex of free factors: it is the space of measure classes of arational trees. (Jointly with T. Coulbois and A. Hilion.)
