Branch locus

Description

For a Branched surface the branch locus is the set of points where branching happens. The branch locus will be defined for a general Branched manifold

Definition

Let $B$ be a branched manifold. The branch locus $\Sigma (B)$ of $B$ is the subset of points whose neighbourhood is not homeomorphic to an ball in ${\mathbb{R}}^n$.

Properties