ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

6. Topology

1991 MS Classification: 54,55 Zastrow, Andreas, Ruhr-University Bochum Planar Sets are Aspherical The talk is about how to tackle possibly very pathological subspaces of IR^{2} in order to prove the result stated in the title. Amongst the techniques involved is the construction of “word sequences“ in our subspace of consideration. In addition, they allow us to choose a minimal representative even for those homotopy classes that cannot be represented by rectifiable paths. These minimal representatives of relative homotopy classes of non-closed paths then enable us to define a contraction of an arbitrary continuous image of a sphere which is the desired result.