The space of cooriented contact elements
WebJan 1, 2003 · A contact element on a manifold is a hyperplane in the tangent space to the manifold at a point. For a surface F we denote by ST ∗ F the space of all cooriented (transversally oriented) contact elements of F. This space is the spherical cotangent bundle of F. Its natural contact structure is the distribution of tangent hyperplanes given by ... WebExamples are given of legendrian links in the manifold of cooriented contact elements of the plane, or equivalently, in the 1-jet space of the circle which are not equivalent via an isotopy of contact diffeomorphisms. These examples have generalizations to linked legendrian spheres in contact manifolds diffeomorphic to R-n x Sn-1. These links are distinguished …
The space of cooriented contact elements
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Webthe space of cooriented contact elements of Σ onto Σ. For a point p∈ Sand a cooriented line Lin TpS, let ξ(p,L) denote the cooriented plane described uniquely by the equation … WebHere is a problem in contact topology that was suggested by Petya's answer to this mathoverflow question of mine. Let S ∗ R n be the space of cooriented contact elements …
WebA contact element at a point of a plane is a line in the tangent plane. Its coorientation is a choice of one of two half-planes into which it divides the tangent plane. The manifold M = ST*ΈL2 of all cooriented contact elements of the plane is diffeomorphic to the solid torus R2 x 51, since the coorienting normal vector is defined by its angle φ. Webform pdq. The manifold P+T∗Mcan also be considered a space of cooriented (n−1)-dimensional contact elements of M. With this interpretation the plane ξ x of ξat a point x= (p,q), q∈ M, p∈ T∗ q (M), consists of infinitesimal deformations of ξ x, which leaves fixed the point of contact q∈ M. Then the
WebIf one has a Riemannian metric on a surface Sthen the bundle of contact elements of S can be identified with the unit tangent bundle STS and the ... ST Swhich, as the notation suggests, can be seen as the space of cooriented contact elements of S. In particular we get an exact filling of the canonical WebJan 1, 2001 · Under the natural pairing defined by the metric g, the space of cooriented contact elements of B may be thought of as the unit cotangent bundle ST*B. There is a …
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WebIn particular, the foliated contact structure restricted to a leaf coincides with the space of contact elements of the leaf. In the same vein, the sphere bundle S = S(T ∗ F) associated to the cotangent space of the foliation is a foliated contact manifold (S, FS , ξS ) that restricts to the space of cooriented contact elements over each leaf. cinnaholic gaithersburgWebWe produce examples of Legendrian isotopy classes in ST∗Rn (the space of cooriented contact elements of Rn, endowed with its standard contact structure) such that any element of those classes has a singular (non-immersed) … diagnostic reference levels meaningWebarXiv:math/9901133v2 [math.GT] 11 Aug 1999 ARNOLD-TYPE INVARIANTS OF WAVE FRONTS ON SURFACES VLADIMIR TCHERNOV Abstract. Recently Arnold’s St and J± invariants of generic plana cinnaholic gift card