On Lagrangian concordance of Legendrian knots

Details On Lagrangian concordance of Legendrian knots On Lagrangian concordance of Legendrian knots

2006-11-28

arxiv.org/abs/math/0611848v2

Mathematics

Symplectic Geometry

21 pages, 5 figures. Minor corrections and a proof of conjecture 6.4 of version 1 (now Theorem 6.4)

Scientific paper

In this article we define Lagrangian concordance of Legendrian knots, the analogue of smooth concordance of knots in the Legendrian category. In particular we study the relation of Lagrangian concordance under Legendrian isotopy. The focus is primarily on the algebraic aspects of the problem. We study the behavior of the classical invariants under this relation, namely the Thurston-Bennequin number and the rotation number, and we provide some examples of non-trivial Legendrian knots bounding Lagrangian surfaces in $D^4$. Using these examples, we are able to provide a new proof of the local Thom conjecture.

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