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Actions of compact connected Lie groups on acyclic manifolds with low dimensional orbit spaces. (English) Zbl 0583.57025
The main results are the following two fixed point theorems: Theorem 1. Let X be an acyclic differentiable G-manifold, G a compact connected Lie group. If dim X/G\(\leq 4\), then F(G,X)\(\neq \emptyset\). Moreover, if \(G\neq SO(3)\), then dim X/G\(\leq 5\) already implies F(G,X)\(\neq \emptyset\). - Theorem 2. Let X be an acyclic differentiable G-manifold. If G does not contain any simple normal factor of rank one and dim X/G\(\leq 11\), then F(G,X)\(\neq \emptyset\).

57S15 Compact Lie groups of differentiable transformations
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