Algebraic & Geometric Topology 6 (2006) 1–69

DOI: 10.2140/agt.2006.6.1

arXiv: math.DG/0410559

Abstract

We prove a generalization of Bennequin’s inequality for Legendrian knots in a 3-dimensional contact manifold (Y,ξ), 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.

Keywords

contact structures, Legendrian knots, Bennequin inequality, excision, monopoles

Mathematical Subject Classification

Primary: 57M25, 57M27, 57R17, 57R57

References

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Publication

Received: 8 November 2005
Accepted: 10 July 2005
Published: 24 February 2006

Authors