Plane curves and contact geometry
@article{Ng2005PlaneCA, title={Plane curves and contact geometry}, author={Lenhard L. Ng}, journal={arXiv: Geometric Topology}, year={2005} }
We apply contact homology to obtain new results in the problem of distinguishing immersed plane curves without dangerous self-tangencies.
2 Citations
Removing cusps from Legendrian front projections
- Mathematics
- 2019
We show that it is possible to isotope certain Legendrian knots of rotation number zero inside the unit cotangent bundle of the plane, i.e. R×S, so that the front projection becomes an immersion. The…
Periodic orbits in the restricted three-body problem and Arnold’s J+-invariant
- Physics
- 2017
We apply Arnold’s theory of generic smooth plane curves to Stark–Zeeman systems. This is a class of Hamiltonian dynamical systems that describes the dynamics of an electron in an external electric…
References
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Topological Invariants of Plane Curves and Caustics
- Mathematics
- 1994
Lecture 1: Invariants and discriminants of plane curves Plane curves Legendrian knots Lecture 2: Symplectic and contact topology of caustics and wave fronts, and Sturm theory Singularities of…
Invariants of Knots, Embeddings and Immersions via Contact Geometry
- Mathematics
- 2004
This paper is an overview of the idea of using contact geometry to construct invariants of immersions and embeddings. In particular, it discusses how to associate a contact manifold to any manifold…
Vassiliev type invariants in arnold's J+-theory of plane curves without direct self-tangencies
- Mathematics
- 1998
Regular Legendrian knots and the HOMFLY polynomial of immersed plane curves
- Mathematics
- 2000
Abstract. We show that every unframed knot type in
$ST^*{\bf \mathrm{R}}^2$ has a representative obtained by the Legendrian lifting of an immersed plane curve. This gives a positive answer to the…
Contact homology and one parameter families of Legendrian knots
- Mathematics
- 2005
We consider S 1 -families of Legendrian knots in the standard contact R 3 . We define the monodromy of such a loop, which is an automorphism of the Chekanov-Eliashberg contact homology of the…
Legendrian solid-torus links
- Mathematics
- 2004
Differential graded algebra invariants are constructed for Legendrian links in the 1-jet space of the circle. In parallel to the theory for R 3 , Poincare-Chekanov polynomials and characteristic al-…
Conormal bundles, contact homology and knot invariants
- Mathematics
- 2004
String theory has provided a beautiful correspondence between enumerative geometryand knot invariants; for details, see the survey by Marino [˜ 16] or other papers in thepresent volume. This…
On Plane Curves
- Mathematics
- 1928
. We collect various known results (about plane curves and the moduli space of stable maps) to derive new recursive formulas enumerating low genus plane curves of any degree with various behaviors.…