Differentiable pseudo-free circle actions.
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.
Institute for Advanced Study, Princeton, N.J. 08540.
D
D
Montgomery
C T
CT
Yang