Foliations with non-compact leaves on surfaces

Abstract

We study non-compact surfaces obtained by gluing strips $\mathbb{R}\times (-1,1)$ with at most countably many boundary intervals along some these intervals. Every such strip possesses a foliation by parallel lines, which gives a foliation on the resulting surface. It is proved that the identity path component of the group of homeomorphisms of that foliation is contractible.

11 pages, 5 figures