Expansive homeomorphisms of compact surfaces are pseudo-Anosov (Q5903849)

The purpose of this paper is to announce the following result. Theorem 1. Every expansive homeomorphism of a compact surface is pseudo-Anosov. If this theorem was established, then by using Euler-Poincaré's formula and Kneser's Theorem, we can give a partial answer to the problem of existence of expansive homeomorphisms as follows. Theorem 2. There are no expansive homeomorphisms on the 2-sphere, the projective plane and the Klein bottle.