A geometric characterization of orientation reversing involutions
Differential Geometry
2014-02-26 v1 Geometric Topology
Abstract
We give a geometric characterization of compact Riemann surfaces admitting orientation reversing involutions with fixed points. Such surfaces are generally called real surfaces and can be represented by real algebraic curves with non-empty real part. We show that there is a family of disjoint simple closed geodesics that intersect all geodesics of a partition at least twice in uniquely right angles if and only if the involution exists. This implies that a surface is real if and only if there is a pants decomposition of the surface with all Fenchel-Nielsen twist parameters equal to 0 or 1/2.
Cite
@article{arxiv.math/0506477,
title = {A geometric characterization of orientation reversing involutions},
author = {Antonio F. Costa and Hugo Parlier},
journal= {arXiv preprint arXiv:math/0506477},
year = {2014}
}
Comments
14 pages, 10 figures