Conformal grafting and convergence of Fenchel-Nielsen twist coordinates

Abstract

We cut a hyperbolic surface of finite area along some analytic simple closed curves, and glue in cylinders of varying moduli. We prove that as the moduli of the glued cylinders go to infinity, the Fenchel-Nielsen twist coordinates for the resulting surface around those cylinders converge.

arXiv comment18 pages, 4 figures