Geometry & Topology
- Geom. Topol.
- Volume 12, Number 1 (2008), 351-386.
Projective structures, grafting and measured laminations
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 () 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.
Geom. Topol., Volume 12, Number 1 (2008), 351-386.
Received: 23 April 2007
Accepted: 20 August 2007
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 30F60: Teichmüller theory [See also 32G15]
Secondary: 30F10: Compact Riemann surfaces and uniformization [See also 14H15, 32G15] 30F40: Kleinian groups [See also 20H10] 32G15: Moduli of Riemann surfaces, Teichmüller theory [See also 14H15, 30Fxx] 57M50: Geometric structures on low-dimensional manifolds
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