Wild singularities of flat surfaces
Geometric Topology
2011-10-07 v1 Differential Geometry
Metric Geometry
Abstract
We consider flat surfaces and the points of their metric completions, particularly the singularities to which the flat structure of the surface does not extend. The local behavior near a singular point x can be partially described by a topological space L(x) which captures all the ways that x can be "approached linearly". The homeomorphism type of L(x) is an affine invariant. When x is not a cone point or an infinite-angle singularity, we say it is wild; in this case it is necessary to add further metric data to L(x) to get a quantitative description of the surface near x.
Cite
@article{arxiv.1110.1350,
title = {Wild singularities of flat surfaces},
author = {Joshua P. Bowman and Ferrán Valdez},
journal= {arXiv preprint arXiv:1110.1350},
year = {2011}
}