ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

6. Topology

1991 MS Classification: 18,55 Turner, Paul, University of Aberdeen, Scotland The homology of spaces representing exact cohomology theories A generalised cohomology theory M^{∗}(−) is exact over another such R^{∗}(−) when for any finite space X we have M^{∗}(X) ≅ R^{∗}(X) ⊗_{R∗(pt)} M^{∗}(pt). All such cohomology theories are represented by infinite loop spaces in the sense that for each k there is an infinite loop space \underline{M}_{k} such that M^{k}(X) ≅ [X, \underline{M}_{k}]. Our interest is in the relationship between the families of spaces \{\underline{M}_{k}\}_{k∈ℤ} and \{\underline{R}_{k}\}_{k∈ℤ} which represent an exact pair of cohomology theories. A precise statement can be given in homology by investigating the theory of coalgebraic modules. These results are joint work with John Hunton. References: (1) J. Hunton and P. Turner, Coalgebraic Algebra, to appear JPAA. (2) J. Hunton and P. Turner, The homology of spaces representing exact pairs of homotopy functors, to appear in Topology.