Legendrian knots and monopoles
Differential Geometry
2009-09-29 v6 Symplectic Geometry
Abstract
We prove a generalization of Bennequin's inequality for Legendrian knots in a 3-dimensional contact manifold (Y,xi), under the assumption that Y is the boundary of a 4-dimensional manifold M and the version of Seiberg-Witten invariants introduced by Kronheimer and Mrowka [Invent. Math. 130 (1997) 209-255] is nonvanishing. The proof requires an excision result for Seiberg-Witten moduli spaces; then the Bennequin inequality becomes a special case of the adjunction inequality for surfaces lying inside M.
Cite
@article{arxiv.math/0410559,
title = {Legendrian knots and monopoles},
author = {Tomasz S Mrowka and Yann Rollin},
journal= {arXiv preprint arXiv:math/0410559},
year = {2009}
}
Comments
This is the version published by Algebraic & Geometric Topology on 24 February 2006