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Projective structures, grafting and measured laminations

David Dumas and Michael Wolf

Geometry and Topology 12 (2008) 351–386

DOI: 10.2140/gt.2008.12.351
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.

Keywords

projective structures, grafting, measured laminations
Mathematical Subject Classification

Primary: 30F60

Secondary: 30F10, 30F40, 32G15, 57M50
References
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/