Extension dimension theory
by
Jerzy Dydak
University of Tennessee

We present a general theory of dimension (called the extension dimension) in terms of extension of maps. Most of the talk is the joint work with A.Dranishnikov. Roughly speaking, dimX <= K means that K is an absolute extensor of X. In particular, dimX <= Sⁿ is equivalent to the covering dimension of X being at most n. dimX=K means that K is minimal with respect to all L such that dimX <= L. It turns out that extension dimension encompassess both the covering dimension and the cohomological dimension. Extension dimension deals with general topological spaces and in the case of finite-dimensional compacta one has an associated algebraic object called the Bockstein algebra. There is a dual theory to extension dimension which deals with CW complexes and in the case of countable CW complexes one has an associated algebraic object called the dual Bockstein algebra.

Date received: January 15, 1998