Stable cohomotopy groups of compact spaces
by
Slawomir Nowak
Warsaw University

Suppose that H = {hⁿ} is a generalized cohomology theory defined on the homotopy category of finite pointed CW complexes.For example the stable cohomotopy groups

\pins(X)= lim { -->   [X, Sn ] --> [ å (X), Sn + 1 ] --> ...}

form such generalized cohomology theory.

The Cech cohomology groups hⁿ(X) of a compact Hausdorff space X are equal to the direct limit of the system {hⁿ(|N( \alpha) |) }, where \alpha varies over the finite open coverings of X.

There are a large number of facts showing that the stable cohomotopy theory has certain universal properties among all generalized (Cech) cohomology theories on compact spaces.

Using stable cohomotopy groups we are also able to characterize compact Hausdorff spaces cohomologically equivalent (isomorphic as objects of the stable shape category) to infinite-dimensional spaces, metrizable spaces or finite CW complexes.

Date received: September 8, 2002

Copyright © 2002 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caje-85.