1,085 research outputs found

    Foliations associated to regular Poisson structures

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    A regular Poisson manifold can be described as a foliated space carrying a tangentially symplectic form. Examples of foliations are produced here that are not induced by any Poisson structure although all the basic obstructions vanish.Comment: 18 pages, postscript fil

    Affine connections and symmetry jets

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    We establish a bijective correspondence between affine connections and a class of semi-holonomic jets of local diffeomorphisms of the underlying manifold called symmetry jets in the text. The symmetry jet corresponding to a torsion free connection consists in the family of 22-jets of the geodesic symmetries. Conversely, any connection is described in terms of the geodesic symmetries by a simple formula involving only the Lie bracket of vector fields. We then formulate, in terms of the symmetry jet, several aspects of the theory of affine connections and obtain geometric and intrinsic descriptions of various related objects involving the gauge groupoid of the frame bundle. In particular, the property of uniqueness of affine extension admits an equivalent formulation as the property of existence and uniqueness of a certain groupoid morphism. Moreover, affine extension may be carried out at all orders and this allows for a description of the tensors associated to an affine connections, namely the torsion, the curvature and their covariant derivatives of all orders, as obstructions for the affine extension to be holonomic. In addition this framework provides a nice interpretation for the absence of other tensors.Comment: 94 pages, 15 figure

    Selling change: advertisements for the 1994 South African election.

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    Paper presented at the Wits History Workshop: Democracy, Popular Precedents, Practice and Culture, 13-15 July, 1994

    One-Act Plays

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