Geometry & Topology

Asymptoticity of grafting and Teichmüller rays

Subhojoy Gupta

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Abstract

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 (2π–) 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.

Article information

Source
Geom. Topol., Volume 18, Number 4 (2014), 2127-2188.

Dates
Received: 23 December 2012
Accepted: 3 February 2014
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513732860

Digital Object Identifier
doi:10.2140/gt.2014.18.2127

Mathematical Reviews number (MathSciNet)
MR3268775

Zentralblatt MATH identifier
1304.30060

Subjects
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

Keywords
grafting rays Teichmüller rays

Citation

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


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