Any Legendrian knot can be C0-perturbed in a direction transverse to the contact planes to obtain a transverse knot. This yields a bijection between the set of isomorphism classes of transverse knots and the set of isomorphism classes of Legendrian knots modulo negative Legendrian stabilization.
Referencesedit
Geiges, Hansjörg (2008). An introduction to contact topology; Volume 109 of Cambridge studies in advanced mathematics. Cambridge University Press. p. 94. ISBN978-0-521-86585-2.
J. Epstein, D. Fuchs, and M. Meyer, Chekanov–Eliashberg invariants and transverse approximations of Legendrian knots, Pacific J. Math. 201 (2001), no. 1, 89–106.
transverse, knot, mathematics, transverse, knot, smooth, embedding, circle, into, three, dimensional, contact, manifold, such, that, tangent, vector, every, point, knot, transverse, contact, plane, that, point, legendrian, knot, perturbed, direction, transvers. In mathematics a transverse knot is a smooth embedding of a circle into a three dimensional contact manifold such that the tangent vector at every point of the knot is transverse to the contact plane at that point Any Legendrian knot can be C0 perturbed in a direction transverse to the contact planes to obtain a transverse knot This yields a bijection between the set of isomorphism classes of transverse knots and the set of isomorphism classes of Legendrian knots modulo negative Legendrian stabilization References editGeiges Hansjorg 2008 An introduction to contact topology Volume 109 of Cambridge studies in advanced mathematics Cambridge University Press p 94 ISBN 978 0 521 86585 2 J Epstein D Fuchs and M Meyer Chekanov Eliashberg invariants and transverse approximations of Legendrian knots Pacific J Math 201 2001 no 1 89 106 nbsp This knot theory related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Transverse knot amp oldid 1058820805, wikipedia, wiki, book, books, library,
