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Differentiable pseudo-free circle actions.

Authors
Type
Published Article
Journal
Proceedings of the National Academy of Sciences of the United States of America
Publication Date
Volume
68
Issue
5
Pages
894–896
Identifiers
PMID: 16591917
Source
Medline

Abstract

The circle group G is said to act pseudofreely if it is not free and if every orbit is one-dimensional and if the isotropy group is the identity except on isolated exceptional orbits where the isotropy group is the finite cyclic group Z(k), k > 1. We consider differentiable actions of this kind on homotopy seven spheres and classify all such actions. As a corollary, it follows that there can be any finite number of exceptional orbits, in contrast to the linear case where there can be at most four.

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