Volume 10, issue 1 (2010)

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Lagrangian concordance of Legendrian knots

Baptiste Chantraine

Algebraic & Geometric Topology 10 (2010) 63–85
Abstract

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 ${D}^{4}$.

Keywords
Legendrian, cobordism, symplectisation, local Thom conjecture
Primary: 57R17
Secondary: 57M50