Geometry & Topology
- Geom. Topol.
- Volume 16, Number 2 (2012), 751-779.
Monopole Floer homology and Legendrian knots
We use monopole Floer homology for sutured manifolds to construct invariants of unoriented Legendrian knots in a contact –manifold. These invariants assign to a knot elements of the monopole knot homology , 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 –manifolds. We also show that these invariants are functorial with respect to Lagrangian concordance.
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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Sivek, Steven. Monopole Floer homology and Legendrian knots. Geom. Topol. 16 (2012), no. 2, 751--779. doi:10.2140/gt.2012.16.751. https://projecteuclid.org/euclid.gt/1513732408