Geometry & Topology 16 (2012) 751–779

DOI: 10.2140/gt.2012.16.751

Abstract

We use monopole Floer homology for sutured manifolds to construct invariants of unoriented Legendrian knots in a contact 3–manifold. These invariants assign to a knot K ⊂ Y elements of the monopole knot homology KHM(−Y,K), and they strongly resemble the knot Floer homology invariants of Lisca, Ozsváth, Stipsicz, and Szabó. We prove several vanishing results, investigate their behavior under contact surgeries, and use this to construct many examples of nonloose knots in overtwisted 3–manifolds. We also show that these invariants are functorial with respect to Lagrangian concordance.

Keywords

Legendrian knot, monopole Floer homology

Mathematical Subject Classification

Primary: 57M27, 57R58

Secondary: 57R17

References

Publication

Received: 5 August 2011
Revised: 3 February 2012
Accepted: 30 January 2012
Published: 2 May 2012
Proposed: Peter S. Ozsváth
Seconded: Yasha Eliashberg, Ronald J. Stern

Authors