Circle Decompositions of Surfaces
arXiv:1009.0575 · doi:10.1016/j.topol.2010.11.015
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.
9 pages, final version, to appear in Topology and its Applications (2010). A few missprints have been corrected