We apply knot Floer homology to exhibit an infinite family of transversely nonsimple prime knots starting with 10132. We also discuss the combinatorial relationship between grid diagrams, braids and Legendrian and transverse knots in standard contact ℝ3.
Khandhawit, Tirasan  1 ; Ng, Lenhard  2
@article{10_2140_agt_2010_10_293,
author = {Khandhawit, Tirasan and Ng, Lenhard},
title = {A family of transversely nonsimple knots},
journal = {Algebraic and Geometric Topology},
pages = {293--314},
year = {2010},
volume = {10},
number = {1},
doi = {10.2140/agt.2010.10.293},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2010.10.293/}
}
TY - JOUR AU - Khandhawit, Tirasan AU - Ng, Lenhard TI - A family of transversely nonsimple knots JO - Algebraic and Geometric Topology PY - 2010 SP - 293 EP - 314 VL - 10 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2010.10.293/ DO - 10.2140/agt.2010.10.293 ID - 10_2140_agt_2010_10_293 ER -
Khandhawit, Tirasan; Ng, Lenhard. A family of transversely nonsimple knots. Algebraic and Geometric Topology, Tome 10 (2010) no. 1, pp. 293-314. doi: 10.2140/agt.2010.10.293
[1] , , Stabilization in the braid groups. II. Transversal simplicity of knots, Geom. Topol. 10 (2006) 1425
[2] , , A note on closed $3$–braids, Commun. Contemp. Math. 10 (2008) 1033
[3] , , On transversally simple knots, J. Differential Geom. 55 (2000) 325
[4] , Embedding knots and links in an open book. I. Basic properties, Topology Appl. 64 (1995) 37
[5] , Arc-presentations of links: monotonic simplification, Fund. Math. 190 (2006) 29
[6] , Legendrian and transversal knots in tight contact $3$–manifolds, from: "Topological methods in modern mathematics (Stony Brook, NY, 1991)" (editors L R Goldberg, A V Phillips), Publish or Perish (1993) 171
[7] , , , Chekanov–Eliashberg invariants and transverse approximations of Legendrian knots, Pacific J. Math. 201 (2001) 89
[8] , Transversal torus knots, Geom. Topol. 3 (1999) 253
[9] , Legendrian and transversal knots, from: "Handbook of knot theory" (editors W Menasco, M Thistlethwaite), Elsevier (2005) 105
[10] , , Knots and contact geometry. I. Torus knots and the figure eight knot, J. Symplectic Geom. 1 (2001) 63
[11] , , Cabling and transverse simplicity, Ann. of Math. $(2)$ 162 (2005) 1305
[12] , , Knotscape
[13] , Braid-positive Legendrian links, Int. Math. Res. Not. (2006) 29
[14] , Connect sum and transversely non simple knots, Math. Proc. Cambridge Philos. Soc. 146 (2009) 661
[15] , , , A combinatorial description of knot Floer homology, Ann. of Math. $(2)$ 169 (2009) 633
[16] , , , Transverse knots distinguished by knot Floer homology, J. Symplectic Geom. 6 (2008) 461
[17] , , Legendrian solid-torus links, J. Symplectic Geom. 2 (2004) 411
[18] , , Markov theorem for transversal links, J. Knot Theory Ramifications 12 (2003) 905
[19] , , , Odd Khovanov homology
[20] , , Contact surgeries and the transverse invariant in knot Floer homology
[21] , , Holomorphic disks and knot invariants, Adv. Math. 186 (2004) 58
[22] , , , Legendrian knots, transverse knots and combinatorial Floer homology, Geom. Topol. 12 (2008) 941
[23] , Floer homology and knot complements, PhD thesis, Harvard University (2003)
[24] , Transversely nonsimple knots, Algebr. Geom. Topol. 8 (2008) 1481
[25] , The Markov Theorem for transverse knots
Cité par Sources :