Grafting, pruning, and the antipodal map on measured laminations
| dc.creator | Dumas, David | |
| dc.date | 2005-01-13 | |
| dc.date | 2006-12-05 | |
| dc.date.accessioned | 2026-07-07T06:39:17Z | |
| dc.date.available | 2026-07-07T06:39:17Z | |
| dc.description | 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 $Γ(i_X)$ of the antipodal involution $i_X : \PML(S) \to \PML(S)$. | |
| dc.description | 25 pages, 4 figures; includes important corrections in sections 9 and 10 | |
| dc.identifier | https://arxiv.org/abs/math/0501194 | |
| dc.identifier | http://arxiv.org/abs/math/0501194 | |
| dc.identifier | J. Differential Geometry, 74 (2006), 93-118 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/101019 | |
| dc.subject | Differential Geometry | |
| dc.subject | 30F60; 53C43 | |
| dc.title | Grafting, pruning, and the antipodal map on measured laminations | |
| dc.type | text |