# Legendrian knots and monopoles

@article{Mrowka2004LegendrianKA,
title={Legendrian knots and monopoles},
author={Tomasz S. Mrowka and Yann Rollin},
journal={Algebraic \& Geometric Topology},
year={2004},
volume={6},
pages={1-69}
}
• Published 26 October 2004
• Mathematics
• Algebraic & Geometric Topology
We prove a generalization of Bennequin’s inequality for Legendrian knots in a 3‐ dimensional contact manifold.Y;/ , 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 in [10] 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 . 57R17, 57M25, 57M27…

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