316 research outputs found

    Basic differential forms for actions of Lie groups

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    A section of a Riemannian GG-manifold MM is a closed submanifold Σ\Sigma which meets each orbit orthogonally. It is shown that the algebra of GG-invariant differential forms on MM which are horizontal in the sense that they kill every vector which is tangent to some orbit, is isomorphic to the algebra of those differential forms on Σ\Sigma which are invariant with respect to the generalized Weyl group of this orbit, under some condition.Comment: 10 pages, ESI Preprint 87, AmSTe

    The homotopy type of the space of degree 0 immersed plane curves

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    The space of all immersed closed curves of rotation degree 0 in the plane modulo reparametrizations has the same homotopy groups as the circle times the 2-sphere.Comment: 7 page