Geometry & Topology
- Geom. Topol.
- Volume 18, Number 4 (2014), 2127-2188.
Asymptoticity of grafting and Teichmüller rays
We show that any grafting ray in Teichmüller space determined by an arational lamination or a multicurve is (strongly) asymptotic to a Teichmüller geodesic ray. As a consequence the projection of a generic grafting ray to the moduli space is dense. We also show that the set of points in Teichmüller space obtained by integer (–) graftings on any hyperbolic surface projects to a dense set in the moduli space. This implies that the conformal surfaces underlying complex projective structures with any fixed Fuchsian holonomy are dense in the moduli space.
Geom. Topol., Volume 18, Number 4 (2014), 2127-2188.
Received: 23 December 2012
Accepted: 3 February 2014
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: 32G15: Moduli of Riemann surfaces, Teichmüller theory [See also 14H15, 30Fxx] 57M50: Geometric structures on low-dimensional manifolds
Gupta, Subhojoy. Asymptoticity of grafting and Teichmüller rays. Geom. Topol. 18 (2014), no. 4, 2127--2188. doi:10.2140/gt.2014.18.2127. https://projecteuclid.org/euclid.gt/1513732860