## Geometry & Topology

### Projective structures, grafting and measured laminations

#### Abstract

We show that grafting any fixed hyperbolic surface defines a homeomorphism from the space of measured laminations to Teichmüller space, complementing a result of Scannell–Wolf on grafting by a fixed lamination. This result is used to study the relationship between the complex-analytic and geometric coordinate systems for the space of complex projective ($ℂℙ1$) structures on a surface.

We also study the rays in Teichmüller space associated to the grafting coordinates, obtaining estimates for extremal and hyperbolic length functions and their derivatives along these grafting rays.

#### Article information

Source
Geom. Topol., Volume 12, Number 1 (2008), 351-386.

Dates
Accepted: 20 August 2007
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513800022

Digital Object Identifier
doi:10.2140/gt.2008.12.351

Mathematical Reviews number (MathSciNet)
MR2390348

Zentralblatt MATH identifier
1147.30030

#### Citation

Dumas, David; Wolf, Michael. Projective structures, grafting and measured laminations. Geom. Topol. 12 (2008), no. 1, 351--386. doi:10.2140/gt.2008.12.351. https://projecteuclid.org/euclid.gt/1513800022

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