By proving a connected sum formula for the Legendrian invariant λ+ in knot Floer homology, we exhibit infinitely many transversely nonsimple knot types.
Vértesi, Vera  1
@article{10_2140_agt_2008_8_1481,
author = {V\'ertesi, Vera},
title = {Transversely nonsimple knots},
journal = {Algebraic and Geometric Topology},
pages = {1481--1498},
year = {2008},
volume = {8},
number = {3},
doi = {10.2140/agt.2008.8.1481},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2008.8.1481/}
}
Vértesi, Vera. Transversely nonsimple knots. Algebraic and Geometric Topology, Tome 8 (2008) no. 3, pp. 1481-1498. doi: 10.2140/agt.2008.8.1481
[1] , , Stabilization in the braid groups. II. Transversal simplicity of knots, Geom. Topol. 10 (2006) 1425
[2] , , Knots, de Gruyter Studies in Math. 5, Walter de Gruyter Co. (2003)
[3] , Differential algebra of Legendrian links, Invent. Math. 150 (2002) 441
[4] , , Classification of topologically trivial Legendrian knots, from: "Geometry, topology, and dynamics (Montreal, PQ, 1995)", CRM Proc. Lecture Notes 15, Amer. Math. Soc. (1998) 17
[5] , , , Chekanov–Eliashberg invariants and transverse approximations of Legendrian knots, Pacific J. Math. 201 (2001) 89
[6] , Legendrian and transversal knots, from: "Handbook of knot theory", Elsevier B. V. (2005) 105
[7] , , Knots and contact geometry. I. Torus knots and the figure eight knot, J. Symplectic Geom. 1 (2001) 63
[8] , , On connected sums and Legendrian knots, Adv. Math. 179 (2003) 59
[9] , , Cabling and transverse simplicity, Ann. of Math. $(2)$ 162 (2005) 1305
[10] , Connect sum and transversely non simple knots
[11] , , , A combinatorial description of knot Floer homology
[12] , , , , On combinatorial link Floer homology
[13] , Computable Legendrian invariants, Topology 42 (2003) 55
[14] , , , Transverse knots distinguished by knot Floer homology
[15] , , Holomorphic discs, link invariants, and the multi-variable Alexander polynomial
[16] , , Holomorphic disks and knot invariants, Adv. Math. 186 (2004) 58
[17] , , Holomorphic disks and topological invariants for closed three-manifolds, Ann. of Math. $(2)$ 159 (2004) 1027
[18] , , , Legendrian knots, transverse knots and combinatorial Floer homology
[19] , Floer homology and knot complements, PhD thesis, Harvard University (2003)
[20] , , An algorithm for computing some Heegaard Floer homologies
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