منابع مشابه
Tame Circle Actions Susan Tolman and Jordan Watts
In this paper, we consider Sjamaar’s holomorphic slice theorem [13], the birational equivalence theorem of Guillemin and Sternberg [7], and a number of important standard constructions that work for Hamiltonian circle actions in both the symplectic category and the Kähler category: reduction, cutting, and blow-up. In each case, we show that the theory extends to Hamiltonian circle actions on co...
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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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Recall that an effective circle action is semifree if the stabilizer subgroup of each point is connected. We show that if (M,ω) is a coadjoint orbit of a compact Lie group G then every element of π1(G) may be represented by a semifree S-action. A theorem of McDuff– Slimowitz then implies that π1(G) injects into π1(Ham(M,ω)), which answers a question raised by Weinstein. We also show that a circ...
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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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Let X be a finitistic space with its rational cohomology isomorphic to that of the wedge sum P (n)∨S or S ∨S∨S. We study continuous S actions on X and determine the possible fixed point sets up to rational cohomology depending on whether or not X is totally non-homologous to zero in XS1 in the Borel fibration X →֒ XS1 −→ BS1 . We also give examples realizing the possible cases.
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2017
ISSN: 0002-9947,1088-6850
DOI: 10.1090/tran/7113