# 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.…