2-Ghastly spaces with the disjoint homotopies property: the method of fractured maps
by
Denise Halverson
Brigham Young University

Codimension one manifold factors are those spaces whose product with a line is a manifold. It is known that if a resolvable generalized manifold has the disjoint homotopies property then it is a codimension one manifold factor. The question of whether or not the converse is true for spaces of dimension n >= 4 is unsolved. Perhaps the most bizarre spaces known to be codimension one manifold factors are the Daverman/Walsh 2-ghastly spaces. These spaces have the property that they contain no embedded 2-manifolds. As a result of this property, previous strategies for demonstrating that spaces have the disjoint homotopies property did not apply. It is now known that there are 2-ghastly spaces with the disjoint homotopies property. The method attack for demonstrating this fact will be discussed.

Date received: January 31, 2001