Denise M. Halverson

Detecting codimension one manifold factors with the disjoint homotopies property

Abstract Codimension one manifold factors are spaces which have the property that their product with R is a manifold. In this paper, the disjoint homotopies property (DHP) is introduced and it is shown that resolvable generalized manifolds with DHP are codimension one manifold factors. For generalized manifolds of dimensions n⩾4 it is shown that DHP is implied by the plentiful 2-manifolds property, a property satisfied by many examples. Furthermore, a new class of codimension one manifold factors, the k-ghastly spaces for k>2, is constructed.

Analyzing the Stability Properties of Kaleidocycles

Kaleidocycles are continuously rotating n-jointed linkages. We consider a certain class of six-jointed kaleidocycles which have a spring at each joint. For this class of kaleidocycles, stored energy varies throughout the rotation process in a nonconstant, cyclic pattern. The purpose of this paper is to model and provide an analysis of the stored energy of a kaleidocycle throughout its motion. In particular, we will solve analytically for the number of stable equilibrium states for any kaleidocycle in this class.

Path concordances as detectors of codimension-one manifold factors

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.

Locally G-homogeneous Busemann G-spaces

We present short proofs of all known topological properties of general Busemann

Detecting codimension one manifold factors with topographical techniques

G

The Steiner Problem on Surfaces of Revolution

-spaces (at present no other property is known for dimensions more than four). We prove that all small metric spheres in locally

Decompositions of {\mathbb {R}^n, n \ge 4} , into Convex Sets Generate Codimension 1 Manifold Factors

G

Detecting codimension one manifold factors with the piecewise disjoint arc-disk property and related properties

-homogeneous Busemann

Heterogeneous Design Optimization From the Microstructure

G

The Bing-Borsuk and the Busemann conjectures ∗

-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