Volume 10, issue 1 (2010)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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 D4.

Keywords
Legendrian, cobordism, symplectisation, local Thom conjecture
Mathematical Subject Classification 2000
Primary: 57R17
Secondary: 57M50
References
Publication
Received: 2 June 2008
Revised: 11 September 2009
Accepted: 15 November 2009
Published: 2 January 2010
Authors
Baptiste Chantraine
Université du Québec à Montréal
Montréal
Canada
H3C 3P8
Université Libre de Bruxelles
Bruxelles
Belgique 1050