The Generalized Schoenflies Theorem for Absolute Suspensions
by
Janusz M. Lysko
Widener University
Coauthors: David P. Bellamy (University of Delaware)

An absolute suspension is a space X such that for all p, q in X there exists a hoemeomorphism h of X onto the suspension of some Y(p, q) such that h(p) and h(q) are the vertices of the suspension. The question (posed by de Groot) whether finite dimensional absolute suspensions are spheres remains open. We prove that the generalized Schoenflies theorem holds for finite dimensional absolute suspensions. The proof follows closely the work of M. Brown who proved this theorem for spheres, but it also contains ideas that go beyond the scope of M. Brown's argument.

Date received: February 24, 2005