Monopole Floer homology and Legendrian knots

Details Monopole Floer homology and Legendrian knots Monopole Floer homology and Legendrian knots

2011-07-29

arxiv.org/abs/1107.6028v1

Mathematics

Symplectic Geometry

27 pages, 9 figures

Scientific paper

We use monopole Floer homology for sutured manifolds to construct invariants of Legendrian knots in a contact 3-manifold. These invariants assign to a knot K in Y elements of the monopole knot homology KHM(-Y,K), and they strongly resemble the knot Floer homology invariants of Lisca, Ozsv\'ath, Stipsicz, and Szab\'o. We prove several vanishing results, investigate their behavior under contact surgeries, and use this to construct many examples of non-loose knots in overtwisted 3-manifolds. We also show that these invariants are functorial with respect to Lagrangian concordance.

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