Grafting, pruning, and the antipodal map on measured laminations

Details Grafting, pruning, and the antipodal map on measured laminations Grafting, pruning, and the antipodal map on measured laminations

2005-01-13

arxiv.org/abs/math/0501194v6

J. Differential Geometry, 74 (2006), 93-118

Mathematics

Differential Geometry

25 pages, 4 figures; includes important corrections in sections 9 and 10

Scientific paper

Grafting a measured lamination on a hyperbolic surface defines a self-map of Teichmuller 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 $X \in \T(S)$, pruning $X$ gives a map $\ML(S) \to \T(S)$. 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 $\CP^1$ structures on $S$. For each $X \in \T(S)$, we show that the boundary of the space $P(X)$ of $\CP^1$ structures on $X$ in the compactification of the grafting coordinates is the graph $\Gamma(i_X)$ of the antipodal involution $i_X : \PML(S) \to \PML(S)$.

Affiliated with

Also associated with

No associations

Rating

Grafting, pruning, and the antipodal map on measured laminations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Grafting, pruning, and the antipodal map on measured laminations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Grafting, pruning, and the antipodal map on measured laminations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-274432