Dimension theory and large Riemannian manifolds (Q1126766)

This is an excellent write-up of a lucid lecture presented by the author at the ICM 98. It begins by an introduction to dimension theory (covering and cohomological) -- an area to which this author has contributed major discoveries in the last decade. The main part of the paper is devoted to recent applications of dimension theory to Novikov conjecture and related problems. A new approach is presented, based on the hypothetical equivalence between asymptotical dimension of a group and the covering dimension of its Higson corona.