The grafting map of Teichmüller space
Published in Journal of the American Mathematical Society, 2002
Recommended citation: Kevin P. Scannell and Michael Wolf. The grafting map of Teichmüller space. Journal of the American Mathematical Society, 15(4):893–927, 2002. https://kevinscannell.com/files/graft.pdf
DOI: doi:10.1090/S0894-0347-02-00395-8
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 Teichmüller 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 Teichmüller space.