ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

6. Topology

1991 MS Classification: 22, 57 Biller, Harald, Universität Stuttgart, Germany Actions of large compact Lie groups on spheres Let G be a compact connected Lie group acting continuously on an n-sphere. (Certain cohomology spheres are admissible.) For sufficiently large G, the Lie algebra 𝔤 or even the equivalence class of the action is determined. Precisely, if dim G ≥ dim SO_{n−4}ℝ+8 then 𝔤 embeds into 𝔬_{n+1}ℝ. The proof involves the classification of transitive actions (A. Borel, 1949 and ’50) and a method due to L. N. Mann (1966). If dim G ≥ dim SO_{n−2}ℝ + 2 then the action is equivalent to the natural action of a closed subgroup of SO_{n+1}ℝ on 𝕊_{n}. This is proved by techniques developed by R. W. Richardson (1961). The results are applied to topological Tits buildings.