Geometry & Topology

Monopole Floer homology and Legendrian knots

Steven Sivek

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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 KY 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.

Article information

Geom. Topol., Volume 16, Number 2 (2012), 751-779.

Received: 5 August 2011
Revised: 3 February 2012
Accepted: 30 January 2012
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M27: Invariants of knots and 3-manifolds 57R58: Floer homology
Secondary: 57R17: Symplectic and contact topology

Legendrian knot monopole Floer homology


Sivek, Steven. Monopole Floer homology and Legendrian knots. Geom. Topol. 16 (2012), no. 2, 751--779. doi:10.2140/gt.2012.16.751.

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