Projective structures, grafting and measured laminations

David Dumas, Michael Wolf
2008 Geometry and Topology  
We show that grafting any fixed hyperbolic surface defines a homeomorphism from the space of measured laminations to Teichmuller 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 Teichmuller space associated to the grafting coordinates, obtaining estimates for
more » ... ing estimates for extremal and hyperbolic length functions and their derivatives along these grafting rays.
doi:10.2140/gt.2008.12.351 fatcat:q4qzotzd7jdrrilakkjcvgu3ca