Lagrangian concordance of Legendrian knots

Chantraine, Baptiste¹

¹Université du Québec à Montréal, Montréal, Canada, H3C 3P8, Université Libre de Bruxelles, Bruxelles, Belgique 1050

Algebraic and Geometric Topology, Tome 10 (2010) no. 1, pp. 63-85

Résumé

In this article, we define the notion of a Lagrangian concordance between two Legendrian knots analogous to smooth concordance in the Legendrian context. We show that Legendrian isotopic Legendrian knots are Lagrangian concordant. The focus is primarily on the algebraic aspects of the problem. We study the behavior of the classical invariants (namely the Thurston–Bennequin number and the rotation number) under this relation, and provide some examples of nontrivial Legendrian knots bounding Lagrangian surfaces in D4.

Détail

DOI : 10.2140/agt.2010.10.63

Keywords: Legendrian, cobordism, symplectisation, local Thom conjecture

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