# Finite-type invariants of Legendrian knots in the 3-space: Maslov index as an order 1 invariant

Victor Goryunov; Jonathan Hill

Banach Center Publications (1999)

- Volume: 50, Issue: 1, page 107-122
- ISSN: 0137-6934

## Access Full Article

top## Abstract

top## How to cite

topGoryunov, Victor, and Hill, Jonathan. "Finite-type invariants of Legendrian knots in the 3-space: Maslov index as an order 1 invariant." Banach Center Publications 50.1 (1999): 107-122. <http://eudml.org/doc/208999>.

@article{Goryunov1999,

abstract = {We consider a contractible closure of the space of Legendrian knots in the standard contact 3-space. We show that in this context the space of finite-type complex-valued invariants of Legendrian knots is isomorphic to that of framed knots in $R^3$ with an extra order 1 generator (Maslov index) added.},

author = {Goryunov, Victor, Hill, Jonathan},

journal = {Banach Center Publications},

keywords = {Legendrian curve; Legendrian knot; finite type invariant; plane front; Vassiliev invariants},

language = {eng},

number = {1},

pages = {107-122},

title = {Finite-type invariants of Legendrian knots in the 3-space: Maslov index as an order 1 invariant},

url = {http://eudml.org/doc/208999},

volume = {50},

year = {1999},

}

TY - JOUR

AU - Goryunov, Victor

AU - Hill, Jonathan

TI - Finite-type invariants of Legendrian knots in the 3-space: Maslov index as an order 1 invariant

JO - Banach Center Publications

PY - 1999

VL - 50

IS - 1

SP - 107

EP - 122

AB - We consider a contractible closure of the space of Legendrian knots in the standard contact 3-space. We show that in this context the space of finite-type complex-valued invariants of Legendrian knots is isomorphic to that of framed knots in $R^3$ with an extra order 1 generator (Maslov index) added.

LA - eng

KW - Legendrian curve; Legendrian knot; finite type invariant; plane front; Vassiliev invariants

UR - http://eudml.org/doc/208999

ER -

## References

top- [1] V. I. Arnol'd, Plane curves, their invariants, perestroikas and classifications, in: Singularities and Bifurcations, V. I. Arnold (ed.), Adv. Soviet Math. 21, Amer. Math. Soc., Providence, 1994, 33-91. Zbl0864.57027
- [2] V. I. Arnol'd, Topological Invariants of Plane Curves and Caustics, University Lecture Series 5, Amer. Math. Soc., Providence, 1994.
- [3] V. I. Arnol'd, Invariants and perestroikas of plane fronts (in Russian), Trudy Mat. Inst. Steklov. 209 (1995), 14-64; English transl.: Proc. Steklov Inst. Mat. 209 (1995), 11-56.
- [4] D. Bar-Natan, On the Vassiliev knot invariants, Topology 34 (1995), 423-472. Zbl0898.57001
- [5] V. V. Goryunov, Vassiliev type invariants in Arnold’s ${J}^{+}$-theory of plane curves without direct self-tangencies, Topology 37 (1998), 603-620. Zbl0909.57002
- [6] V. V. Goryunov, Vassiliev invariants of knots in ${R}^{3}$ and in a solid torus, in: Differential and Symplectic Topology of Knots and Curves, S. Tabachnikov (ed.), Amer. Math. Soc. Transl. Ser. 2, 190, Amer. Math. Soc., Providence, 1999, 37-59. Zbl0946.57017
- [7] V. V. Goryunov, Finite order invariants of framed knots in a solid torus and in Arnold’s ${J}^{+}$-theory of plane curves, in: Geometry and Physics, J. E. Andersen, J. Dupont, H. Pedersen and A. Swann (eds.), Lecture Notes in Pure and Appl. Math. 184, Marcel Dekker, New York, 1997, 549-556. Zbl0871.57007
- [8] J. W. Hill, Vassiliev-type invariants of planar fronts without dangerous self-tangencies, C. R. Acad. Sci. Paris Sér. I Math. 324 (1997), 537-542. Zbl0881.57003
- [9] M. Kontsevich, Vassiliev's knot invariants, in: I. M. Gel'fand Seminar, S. Gel'fand, S. Gindikin (eds.), Adv. Soviet Math. 16, Part 2, Amer. Math. Soc., Providence, 1993, 137-150. Zbl0839.57006
- [10] V. A. Vassiliev, Cohomology of knot spaces, in: Theory of Singularities and its Applications, V. I. Arnol'd (ed.), Adv. Soviet Math. 1, Amer. Math. Soc., Providence, 1990, 23-69.

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.