On Some Branched Surfaces Which Admit Expanding Immersions

Abstract

We deal with the class of branched surfaces $K$ such that 1) the branch set $S$ of $K$ is an embedded circle, 2) all connected components of $K\backslash S$ are orientable and their number is two or three. We show that in this class only two topological types admit expanding immersions. In the proof of the result, the Euler class of the tangent bundle of $K$ plays an important role.