The grafting map of Teichmuller space
Differential Geometry
2007-05-23 v1 Complex Variables
Geometric Topology
Abstract
Grafting is a method of obtaining new projective structures from a hyperbolic structure, basically by gluing a flat cylinder into a surface along a closed geodesic in the hyperbolic structure, or by limits of that procedure. This induces a map of Teichmuller space to itself. We prove that this map is a homeomorphism by analyzing harmonic maps between pairs of grafted surfaces. As a corollary we obtain bending coordinates for the Bers embedding of Teichmuller space.
Cite
@article{arxiv.math/9810082,
title = {The grafting map of Teichmuller space},
author = {Kevin P. Scannell and Michael Wolf},
journal= {arXiv preprint arXiv:math/9810082},
year = {2007}
}
Comments
31 pages, no figures