Monopole Floer homology and Legendrian knots

Sivek, Steven

doi:10.2140/gt.2012.16.751

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Monopole Floer homology and Legendrian knots

Steven Sivek

Geometry & Topology 16 (2012) 751–779

DOI: 10.2140/gt.2012.16.751

Correction: 10.2140/gt.2015.19.495

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 $K \subset Y$ elements of the monopole knot homology $K H M (- Y, K)$ , 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 2010

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

Correction: 27 February 2015

Authors

Steven Sivek
Department of Mathematics Harvard University Cambridge, MA 02138 USA
http://math.harvard.edu/~ssivek

Volume 16, issue 2 (2012)