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On rotation of vector fields equivariant with respect to transformation groups. (Russian) Zbl 0602.57016

Three theorems on the rotation of vector fields equivariant with respect to transformations of arbitrary groups are proved. These results are generalizations of analogous results for finite groups.
Theorem 1. Let G, G’ be arbitrary transformation groups on \(S^{n-1}\), \(\phi\), \(\psi\) semi-homotopic equivariant vector fields. Then \(\gamma (\phi)=\gamma (\psi)\) (mod \(\pi\) (G)), where \(\pi\) (G) is the \(\pi\)- characteristic of the group G.
Theorem 3. Let \(\phi\) be an equivariant vector field. Then \(\gamma (\phi)=k\), if \(n=2\); and \(=k\gamma (\phi_ 0)\), if \(n>2\), where \(\gamma (\phi_ 0)\) is the rotation of the narrowing of \(\phi\) on the sphere \(S^{n-3}\).
Reviewer: A.S.Potapov

MSC:

57R25 Vector fields, frame fields in differential topology
57S99 Topological transformation groups
57S25 Groups acting on specific manifolds
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