Lagrangian concordance of Legendrian knots

Chantraine, Baptiste

doi:10.2140/agt.2010.10.63

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Lagrangian concordance of Legendrian knots

Baptiste Chantraine

Algebraic & Geometric Topology 10 (2010) 63–85

DOI: 10.2140/agt.2010.10.63

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

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

Volume 10, issue 1 (2010)