Geodesic
Transverse-Legendrian links
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1960-1980.

Voir la notice de l'article provenant de la source Math-Net.Ru

In recent joint works of the present author with M. Prasolov and V. Shastin a new technique for distinguishing Legendrian knots has been developed. In this paper the technique is extended further to provide a tool for distinguishing transverse knots. It is shown that the equivalence problem for transverse knots with trivial orientation-preserving symmetry group is algorithmically solvable. In a future paper the triviality condition for the orientation-preserving symmetry group will be dropped.
Keywords: Legendrian link, rectangular diagram.
Mots-clés : transverse link 
@article{SEMR_2019_16_a61,
     author = {I. A. Dynnikov},
     title = {Transverse-Legendrian links},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1960--1980},
     publisher = {mathdoc},
     volume = {16},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a61/}
}
TY  - JOUR
AU  - I. A. Dynnikov
TI  - Transverse-Legendrian links
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2019
SP  - 1960
EP  - 1980
VL  - 16
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2019_16_a61/
LA  - ru
ID  - SEMR_2019_16_a61
ER  - 
%0 Journal Article
%A I. A. Dynnikov
%T Transverse-Legendrian links
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2019
%P 1960-1980
%V 16
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2019_16_a61/
%G ru
%F SEMR_2019_16_a61
I. A. Dynnikov. Transverse-Legendrian links. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1960-1980. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a61/

[1] J. Birman, W. Menasco, “Studying links via closed braids. IV. Composite links and split links”, Invent. Math., 102:1 (1990), 115–139 | DOI | MR | Zbl

[2] W. Chongchitmate, L. Ng, “An atlas of Legendrian knots”, Exp. Math., 22:1 (2013), 26–37, arXiv: 1010.3997 [math.SG] | DOI | MR | Zbl

[3] P. Cromwell, “Embedding knots and links in an open book. I. Basic properties”, Topology Appl., 64:1 (1995), 37–58 | DOI | MR | Zbl

[4] I. Dynnikov, “Arc-presentations of links: Monotonic simplification”, Fundam. Math., 190 (2006), 29–76, arXiv: math/0208153 [math.GT] | DOI | MR | Zbl

[5] Trans. Moscow Math. Soc., 74:2 (2013), 97–144, arXiv: 1206.0898 [math.GT] | MR | Zbl

[6] I. Dynnikov, M. Prasolov, Rectangular diagrams of surfaces: distinguishing Legendrian knots, arXiv: 1712.06366 [math.GT] | MR

[7] I. Dynnikov, V. Shastin, Distinguishing Legendrian knots with trivial orientation-preserving symmetry group, arXiv: 1810.06460 [math.GT]

[8] J. Etnyre, “Legendrian and transversal knots”, Handbook of knot theory, Elsevier, Amsterdam, 2005, 105–185 | DOI | MR | Zbl

[9] H. Geiges, An Introduction to Contact Topology, Cambridge University Press, Cambridge, 2008 | MR | Zbl

[10] P. Ozsváth, Z. Szabó, D. Thurston, “Legendrian knots, transverse knots and combinatorial Floer homology”, Geometry and Topology, 12:2 (2008), 941–980, arXiv: math/0611841 [math.GT] | DOI | MR | Zbl