74,014 research outputs found

    Hamiltonian circle actions with minimal isolated fixed points

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    Let the circle act in a Hamiltonian fashion on a compact symplectic manifold (M,Ο‰)(M, \omega) of dimension 2n2n. Then the S1S^1-action has at least n+1n+1 fixed points. We study the case when the fixed point set consists of precisely n+1n+1 isolated points. We show certain equivalence on the first Chern class of MM and some particular weight of the S1S^1-action at some fixed point. We show that the particular weight can completely determine the integral cohomology ring of MM, the total Chern class of MM, and the sets of weights of the S1S^1-action at all the fixed points. We will see that all these data are isomorphic to those of known examples, \CP^n, or \Gt_2(\R^{n+2}) with nβ‰₯3n\geq 3 odd, equipped with standard circle actions.Comment: title is slightly changed. Some contents are change

    Twisted Topological Graph Algebras

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    We define the notion of a twisted topological graph algebra associated to a topological graph and a 11-cocycle on its edge set. We prove a stronger version of a Vasselli's result. We expand Katsura's results to study twisted topological graph algebras. We prove a version of the Cuntz-Krieger uniqueness theorem, describe the gauge-invariant ideal structure. We find that a twisted topological graph algebra is simple if and only if the corresponding untwisted one is simple.Comment: 27 page

    The fundamental groups of contact toric manifolds

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    Let MM be a connected compact contact toric manifold. Most of such manifolds are of Reeb type. We show that if MM is of Reeb type, then Ο€1(M)\pi_1(M) is finite cyclic, and we describe how to obtain the order of Ο€1(M)\pi_1(M) from the moment map image.Comment: This version is the published on
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