Geometry & Topology

Projective structures, grafting and measured laminations

David Dumas and Michael Wolf

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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 (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.

Article information

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

Dates
Received: 23 April 2007
Accepted: 20 August 2007
First available in Project Euclid: 20 December 2017

Permanent link to this document
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

Subjects
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

Keywords
projective structures grafting measured laminations

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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