منابع مشابه
Taming Free Circle Actions
It is shown that an arbitrary free action of the circle group on a closed manifold of dimension at least six is concordant to a "tame" action (so that the orbit space is a manifold). A consequence is that the concordance classification of arbitrary free actions of the circle on a simply connected manifold is the same as the equivariant homeomorphism classification of free tame actions. Consider...
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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...
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Consider an effective Hamiltonian circle action on a compact symplectic 2n-dimensional manifold (M, ω). Assume that the fixed set M 1 is minimal, in two senses: it has exactly two components, X and Y , and dim(X) + dim(Y ) = dim(M)− 2. We prove that the integral cohomology ring and Chern classes of M are isomorphic to either those of CP or to those of e G2(R), where e G2(R) denotes the Grassman...
متن کاملFixed-Point Free Circle Actions on 4-Manifolds
This paper is concerned with fixed-point free S-actions (smooth or locally linear) on orientable 4-manifolds. We show that the fundamental group plays a predominant role in the equivariant classification of such 4-manifolds. In particular, it is shown that for any finitely presented group with infinite center, there are at most finitely many distinct smooth (resp. topological) 4-manifolds which...
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We prove that closed symplectic four-manifolds do not admit any smooth free circle actions with contractible orbits, without assuming that the actions preserve the symplectic forms. In higher dimensions such actions by symplectomorphisms do exist, and we give explicit examples based on the constructions of [5].
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ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 2000
ISSN: 0019-2082
DOI: 10.1215/ijm/1255984692