Stable shape: applications and open problems
by
Slawomir Nowak
Institute of Mathematics, University of Warsaw

The stable shape category ShStab of compact spaces is related to stable homotopy as the ordinary shape category Sh is to homotopy.

The purpose of the talk is to present properties of ShStab. The special emphasis is put on interactions of stable shape with other areas of topology. This approach motives us to introduce new shape or stable shape invariants and modify the construction of ShStab.

In particular the infinite dimensional stable shape categories of compact spaces are defined. In certain sense they are complementary to n-shape category of compact spaces (finite dimensional shape category). The objects of infinite dimensional shape category are isomorphic iff their function spectra have the same n-type.

We formulate open problems which concern relationships between shape or stable shape theory and topology or homotopy theory.

Date received: April 27, 2008