Disjoint Homotopies Results for Generalized Manifolds
by
Denise Halverson
University of Tennessee at Knoxville

A generalized manifold X has Disjoint Homotopies Property (DHP) if given any two homotopies g_t, h_t :I = [0, 1] --> X and \epsilon > 0, there are homotopies G_t, H_t :I --> X such that d(G_t, g_t) < \epsilon,   d(H_t, h_t) < \epsilon and G_t(I) \cap H_t(I) = \emptyset for all t in I.
The following results will be discussed:
1) If X is a resolvable generalized n- manifold, n >= 4, with DHP, then X ×R¹ has disjoint disks property (DDP).
2) If X is a resolvable generalized n- manifold, n >= 4, with the property that for any f :I --> X and \epsilon > 0, there is a 2-manifold N subset X and map F :I --> N such that d(F, f) < \epsilon, then X has DHP.

Date received: February 6, 1998