On Shikata's distance between differentiable structures

Shikata proved: there is a number (n) with the following property: If two compact homeomorphic n-dimensional manifolds have a distance less than (n), then they are diffeomorphic. We improve the known lower bound (n!)^–n for (n) to 1/3n ^–2.This work was done under the program Sonderforschungsbereich Theoretische Mathematik (SFB 40) at Bonn University while Shikata was SFB-guest at Bonn.