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
We present a new property, the Disjoint Path Concordances Property, of an ENR
homology manifold X which precisely characterizes when X times R has the
Disjoint Disks Property. As a consequence, X times R is a manifold if and only
if X is resolvable and it possesses this Disjoint Path Concordances Property.Comment: This is the version published by Geometry & Topology Monographs on 22
April 200
We present short proofs of all known topological properties of general Busemann G-spaces (at present no other property is known for dimensions more than four). We prove that all small metric spheres in locally G-homogeneous Busemann G-spaces are homeomorphic and strongly topologically homogeneous. This is a key result in the context of the classical Busemann conjecture concerning the characterization of topological manifolds, which asserts that every n-dimensional Busemann G-space is a topological nmanifold. We also prove that every Busemann G-space which is uniformly locally G-homogeneous on an orbal subset must be finite-dimensional.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.