Legendrian knots and monopoles

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.

This is the version published by Algebraic & Geometric Topology on 24 February 2006

References in corpus (1)

• An infinite family of tight, not semi-fillable contact three-manifolds

Cited by in corpus (12)

• Instanton Floer homology and contact structures
• Maximal contact and symplectic structures
• Bennequin type inequalities in lens spaces
• Monopole Floer homology and Legendrian knots
• Naturality of the Contact Invariant in Monopole Floer Homology Under Strong Symplectic Cobordisms
• On contact type hypersurfaces in 4-space
• A Bauer-Furuta type refinement of Kronheimer-Mrowka's invariant for 4-manifolds with contact boundary
• No homotopy 4-sphere invariants using ECH = SWF
• 4-dimensional aspects of tight contact 3-manifolds
• Exotic Dehn twists on sums of two contact 3-manifolds
• A monopole invariant for families of contact structures
• On naturality of the Ozsvath-Szabo contact invariant