Geodesic
Rectangular Diagrams of Giroux Convex Surfaces
Informatics and Automation, Geometry, Topology, and Mathematical Physics, Tome 325 (2024), pp. 146-174 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We show that any two rectangular diagrams of equivalent Giroux convex surfaces with Legendrian boundary in the three-sphere can be obtained from each other by a sequence of basic moves preserving their equivalence class.
Mots-clés : Giroux convex surface
Keywords: rectangular diagram of a surface. 
@article{TRSPY_2024_325_a7,
     author = {Ivan A. Dynnikov and Maxim V. Prasolov},
     title = {Rectangular {Diagrams} of {Giroux} {Convex} {Surfaces}},
     journal = {Informatics and Automation},
     pages = {146--174},
     year = {2024},
     volume = {325},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2024_325_a7/}
}
TY  - JOUR
AU  - Ivan A. Dynnikov
AU  - Maxim V. Prasolov
TI  - Rectangular Diagrams of Giroux Convex Surfaces
JO  - Informatics and Automation
PY  - 2024
SP  - 146
EP  - 174
VL  - 325
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2024_325_a7/
LA  - ru
ID  - TRSPY_2024_325_a7
ER  - 
%0 Journal Article
%A Ivan A. Dynnikov
%A Maxim V. Prasolov
%T Rectangular Diagrams of Giroux Convex Surfaces
%J Informatics and Automation
%D 2024
%P 146-174
%V 325
%U http://geodesic.mathdoc.fr/item/TRSPY_2024_325_a7/
%G ru
%F TRSPY_2024_325_a7
Ivan A. Dynnikov; Maxim V. Prasolov. Rectangular Diagrams of Giroux Convex Surfaces. Informatics and Automation, Geometry, Topology, and Mathematical Physics, Tome 325 (2024), pp. 146-174. http://geodesic.mathdoc.fr/item/TRSPY_2024_325_a7/

[1] Bennequin D., “Entrelacements et équations de Pfaff”, Astérisque, 107–108 (1983), 87–161 | MR | Zbl

[2] Dynnikov I.A., “Arc-presentations of links: Monotonic simplification”, Fundam. math., 190 (2006), 29–76 ; arXiv: ; arXiv: math/0208153 [math.GT]1206.0898 [math.GT] | DOI | MR | Zbl | DOI | DOI

[3] I. A. Dynnikov and M. V. Prasolov, “Bypasses for rectangular diagrams. A proof of the Jones conjecture and related questions”, Trans. Moscow Math. Soc., 2013 (2013), 97–144 ; arXiv: 1606.03497 [math.GT] | DOI | MR | MR | Zbl | DOI | DOI

[4] I. A. Dynnikov and M. V. Prasolov, “Rectangular diagrams of surfaces: Representability”, Sb. Math., 208:6 (2017), 791–841 | DOI | DOI | DOI | MR | Zbl

[5] Dynnikov I., Prasolov M., “Rectangular diagrams of surfaces: The basic moves”, Proc. Int. Geom. Cent., 13:4 (2020), 50–88 | DOI | MR | Zbl

[6] Dynnikov I., Prasolov M., “Rectangular diagrams of surfaces: Distinguishing Legendrian knots”, J. Topol., 14:3 (2021), 701–860 ; arXiv: 1712.06366 [math.GT] | DOI | MR | Zbl | DOI

[7] Dynnikov I., Prasolov M., An algorithm for comparing Legendrian knots, E-print, 2023, arXiv: 2309.05087 [math.GT] | DOI | MR

[8] I. A. Dynnikov and V. A. Shastin, “On equivalence of Legendrian knots”, Russ. Math. Surv., 73:6 (2018), 1125–1127 | DOI | DOI | MR | Zbl

[9] Dynnikov I., Shastin V., “Distinguishing Legendrian knots with trivial orientation-preserving symmetry group”, Algebr. Geom. Topol., 23:4 (2023), 1849–1889 ; arXiv: 1810.06460 [math.GT] | DOI | MR | Zbl | DOI

[10] Giroux E., “Convexité en topologie de contact”, Comment. math. Helv., 66:4 (1991), 637–677 | DOI | MR | Zbl

[11] Giroux E., “Structures de contact en dimension trois et bifurcations des feuilletages de surfaces”, Invent. math., 141:3 (2000), 615–689 | DOI | MR | Zbl

[12] Honda K., “On the classification of tight contact structures. I”, Geom. Topol., 4 (2000), 309–368 ; arXiv: math/9910127 [math.DG] | DOI | MR | Zbl | DOI

[13] Honda K., “Gluing tight contact structures”, Duke Math. J., 115:3 (2002), 435–478 ; arXiv: math/0102029 [math.GT] | DOI | MR | Zbl | DOI

[14] Menasco W.W., “On iterated torus knots and transversal knots”, Geom. Topol., 5 (2001), 651–682 | DOI | MR | Zbl

[15] Prasolov M., “Rectangular diagrams of Legendrian graphs”, J. Knot Theory Ramifications, 23:13 (2014), 1450074 | DOI | MR | Zbl