Circle Decompositions of Surfaces
General Topology
2011-01-04 v2 Geometric Topology
Abstract
We determine which connected surfaces can be partitioned into topological circles. There are exactly seven such surfaces up to homeomorphism: those of finite type, of Euler characteristic zero, and with compact boundary components. As a byproduct, we get that any circle decomposition of a surface is upper semicontinuous.
Cite
@article{arxiv.1009.0575,
title = {Circle Decompositions of Surfaces},
author = {Gábor Moussong and Nándor Simányi},
journal= {arXiv preprint arXiv:1009.0575},
year = {2011}
}
Comments
9 pages, final version, to appear in Topology and its Applications (2010). A few missprints have been corrected