Legendrian graphs and quasipositive diagrams

Sebastian Baader[1]; Masaharu Ishikawa[2]

  • [1] Department of Mathematics, ETH Zürich, Switzerland
  • [2] Mathematical Institute, Tohoku University, Sendai, 980-8578, Japan

Annales de la faculté des sciences de Toulouse Mathématiques (2009)

  • Volume: 18, Issue: 2, page 285-305
  • ISSN: 0240-2963

Abstract

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In this paper we clarify the relationship between ribbon surfaces of Legendrian graphs and quasipositive diagrams by using certain fence diagrams. As an application, we give an alternative proof of a theorem concerning a relationship between quasipositive fiber surfaces and contact structures on S 3 . We also answer a question of L. Rudolph concerning moves of quasipositive diagrams.

How to cite

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Baader, Sebastian, and Ishikawa, Masaharu. "Legendrian graphs and quasipositive diagrams." Annales de la faculté des sciences de Toulouse Mathématiques 18.2 (2009): 285-305. <http://eudml.org/doc/10110>.

@article{Baader2009,
abstract = {In this paper we clarify the relationship between ribbon surfaces of Legendrian graphs and quasipositive diagrams by using certain fence diagrams. As an application, we give an alternative proof of a theorem concerning a relationship between quasipositive fiber surfaces and contact structures on $S^3$. We also answer a question of L. Rudolph concerning moves of quasipositive diagrams.},
affiliation = {Department of Mathematics, ETH Zürich, Switzerland; Mathematical Institute, Tohoku University, Sendai, 980-8578, Japan},
author = {Baader, Sebastian, Ishikawa, Masaharu},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {contact structure; fiber surface; Legendrian graph},
language = {eng},
month = {1},
number = {2},
pages = {285-305},
publisher = {Université Paul Sabatier, Toulouse},
title = {Legendrian graphs and quasipositive diagrams},
url = {http://eudml.org/doc/10110},
volume = {18},
year = {2009},
}

TY - JOUR
AU - Baader, Sebastian
AU - Ishikawa, Masaharu
TI - Legendrian graphs and quasipositive diagrams
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2009/1//
PB - Université Paul Sabatier, Toulouse
VL - 18
IS - 2
SP - 285
EP - 305
AB - In this paper we clarify the relationship between ribbon surfaces of Legendrian graphs and quasipositive diagrams by using certain fence diagrams. As an application, we give an alternative proof of a theorem concerning a relationship between quasipositive fiber surfaces and contact structures on $S^3$. We also answer a question of L. Rudolph concerning moves of quasipositive diagrams.
LA - eng
KW - contact structure; fiber surface; Legendrian graph
UR - http://eudml.org/doc/10110
ER -

References

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  1. Akbulut (S.), Ozbagci (B.).— Lefschetz fibrations on compact Stein surfaces, Geometry & Topology 5, p. 319-334 (2001). Zbl1002.57062MR1825664
  2. Chekanov (Y.).— Differential algebra of Legendrian links, Invent. Math. 150, p. 441-483 (2002). Zbl1029.57011MR1946550
  3. Eliashberg (Y.), Fraser (M.).— Classification of topologically trivial Legendrian knots, in Geometry, topology, and dynamics (Montreal, PQ, 1995), pp. 17-51, CRM Proc. Lecture Notes 15, A.M.S., Providence, RI, (1998). Zbl0907.53021MR1619122
  4. Etnyre (J.B.).— Lectures on open book decompositions and contact structures, Floer homology, gauge theory, and low-dimensional topology, pp. 103-141, Clay Math. Proc., 5, A.M.S., Providence, RI, 2006. Zbl1108.53050MR2249250
  5. Etnyre (J.B.), Honda (K.).— Knots and contact geometry. I. Torus knots and the figure eight knot, J. Symplectic Geom. 1, p. 63-120 (2001). Zbl1037.57021MR1959579
  6. Giroux (E.).— Convexité en topologie de contact, Comment. Math. Helvetici 66, p. 637-677 (1991). Zbl0766.53028MR1129802
  7. Giroux (E.).— Géométrie de contact : de la dimension trois vers dimensions supérieures, Proceedings of the International Congress of Mathematicians, Vol II (Beijing, 2002), pp.405-414, Higher Ed. Press, Beijing, (2002). Zbl1015.53049MR1957051
  8. Gompf (R.E.).— Handlebody construction of Stein surfaces, Ann. of Math. 148, p. 619-693 (1998). Zbl0919.57012MR1668563
  9. Goodman (N.).— Contact structures and open books, Ph. D thesis, UT Austin, (2003). 
  10. Harer (J.).— How to construct all fibered knots and links, Topology 21, p. 263-280 (1982). Zbl0504.57002MR649758
  11. Hedden (M.).— Notions of positivity and the Ozsváth-Szabó concordance invariant, to appear in J. Knot Theory Ramifications, available at: arXiv.math.GT/0509499. MR2372849
  12. Hedden (M.).— Some remarks on cabling, contact structures, and complex curves, to appear in Proc. Gökova Geom. Topol. Conference, 2007, available at: arXiv.math.GT/0804.4327. Zbl1187.57005
  13. Ng (L.L.).— Computable Legendrian invariants, Topology 42 (2003), no. 1, 55-82. Zbl1032.53070MR1928645
  14. D. Rolfsen, Knots and links, Mathematics Lecture Series 7, Publish or Perish, Inc., Berkeley, Calif., (1976). Zbl0339.55004MR1277811
  15. Rudolph (L.).— Quasipositive plumbing (Constructions of quasipositive knots and links, V), Proc. A.M.S. 126, p. 257-267 (1998). Zbl0888.57010MR1452826
  16. Światkowski (J.).— On the isotopy of Legendrian knots, Ann. Glob. Anal. Geom. 10, p. 195-207 (1992). Zbl0766.53030MR1186009
  17. Torisu (I.).— Convex contact structures and fibered links in 3-manifolds, Int. Math. Res. Not. 9, p. 441-454 (2000). Zbl0978.53133MR1756943

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