Holonomy limits of complex projective structures
Abstract
We study the limits of holonomy representations of complex projective structures on a compact Riemann surface in the Morgan-Shalen compactification of the character variety. We show that the dual R-trees of the quadratic differentials associated to a divergent sequence of projective structures determine the Morgan-Shalen limit points up to a natural folding operation. For quadratic differentials with simple zeros, no folding is possible and the limit of holonomy representations is isometric to the dual tree. We also derive an estimate for the growth rate of the holonomy map in terms of a norm on the space of quadratic differentials.
Keywords
Cite
@article{arxiv.1105.5102,
title = {Holonomy limits of complex projective structures},
author = {David Dumas},
journal= {arXiv preprint arXiv:1105.5102},
year = {2015}
}
Comments
44 pages, 3 figures. V3: Revised according to referee report; geometric limit argument now uses the asymptotic cone (following Chiswell and Kapovich-Leeb)