#### Volume 12, issue 1 (2008)

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Projective structures, grafting and measured laminations

### David Dumas and Michael Wolf

Geometry & Topology 12 (2008) 351–386
##### 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 (${ℂℙ}^{1}$) 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.

##### Keywords
projective structures, grafting, measured laminations
##### Mathematical Subject Classification 2000
Primary: 30F60
Secondary: 30F10, 30F40, 32G15, 57M50
##### Publication
Received: 23 April 2007
Accepted: 20 August 2007
Published: 12 March 2008
Proposed: Jean-Pierre Otal
Seconded: Benson Farb, Martin Bridson
##### Authors
 David Dumas Department of Mathematics Brown University Providence RI 02912 USA http://www.math.brown.edu/~ddumas/ Michael Wolf Department of Mathematics Rice University Houston TX 77005 USA http://www.math.rice.edu/~mwolf/