Legendrian knots and monopoles
Abstract
We prove a generalization of Bennequin's inequality for Legendrian knots in a 3dimensional contact manifold (Y,xi), under the assumption that Y is the boundary of a 4dimensional manifold M and the version of SeibergWitten invariants introduced by Kronheimer and Mrowka [Invent. Math. 130 (1997) 209255] is nonvanishing. The proof requires an excision result for SeibergWitten moduli spaces; then the Bennequin inequality becomes a special case of the adjunction inequality for surfaces lying inside M.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 October 2004
 arXiv:
 arXiv:math/0410559
 Bibcode:
 2004math.....10559M
 Keywords:

 Mathematics  Differential Geometry;
 Mathematics  Symplectic Geometry;
 57M25;
 57M27;
 57R17;
 57R57
 EPrint:
 This is the version published by Algebraic &