We prove recognition theorems for codimension one manifold factors of
dimension $n \geq 4$. 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 $X
\times \mathbb{R}$ is a manifold in the cases when $X$ is a resolvable
generalized manifold of finite dimension $n \geq 3$ 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.