Detecting codimension one manifold factors with topographical techniques

We prove recognition theorems for codimension one manifold factors of dimension $n\ge 4$. In particular, we formalize topographical methods and introduce three ribbons properties: the crinkled ribbons property, the twisted crinkled ribbons property, and the fuzzy ribbons property. We show that $X \times $\mathbb{R}$$isamanifoldinthecaseswhen$X$ is a resolvable generalized manifold of finite dimension $n\ge 3$ with either: (1) the crinkled ribbons property; (2) the twisted crinkled ribbons property and the disjoint point disk property; or (3) the fuzzy ribbons property.