### Grafting, Pruning, and the Antipodal Map on Measured Laminations

#### Abstract:

Grafting a measured lamination on a hyperbolic surface defines a self-map of Teichmüller space, which is a homeomorphism by a result of Scannell and Wolf. In this paper we study the large-scale behavior of pruning, which is the inverse of grafting.

Specifically, for each conformal structure X T(S), pruning X gives a map ML(S)T(S). We show that this map extends to the Thurston compactification of T(S), and that its boundary values are the natural antipodal involution relative to X on the space of projective measured laminations.

We use this result to study Thurston's grafting coordinates on the space of 1 structures on S. For each X T(S), we show that the boundary of the space P(X) of 1 structures on X in the compactification of the grafting coordinates is the graph (iX) of the antipodal involution iX : ML(S)ML(S).