The homeomorphism problem for closed manifolds
by
F.T. Farrell
Binghamton University

We will discuss the following basic problem for closed manifolds M and N. Find calculable invariants which imply that M and N are homeomorphic. We will assume that M and N are homotopically equivalent. Work of Moise leads us to focus on two opposite cases. First, M is simply connected. Second, M is aspherical. In the first case, we review Novikov's solution to the Hurewicz Conjecture. In the second case, we discuss some partial results on Borel's Conjecture.

Date received: February 4, 1998