• Corpus ID: 1540348

Plane curves and contact geometry

@article{Ng2005PlaneCA,
  title={Plane curves and contact geometry},
  author={Lenhard L. Ng},
  journal={arXiv: Geometric Topology},
  year={2005}
}
  • Lenhard L. Ng
  • Published 8 March 2005
  • Mathematics
  • arXiv: Geometric Topology
We apply contact homology to obtain new results in the problem of distinguishing immersed plane curves without dangerous self-tangencies. 

Figures from this paper

Removing cusps from Legendrian front projections
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
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

SHOWING 1-10 OF 21 REFERENCES
Topological Invariants of Plane Curves and Caustics
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
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
Regular Legendrian knots and the HOMFLY polynomial of immersed plane curves
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
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
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
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
. 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.
...
...