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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Monopole Floer homology and Legendrian knots

Steven Sivek

Geometry & Topology 16 (2012) 751–779
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 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
Authors
Steven Sivek
Department of Mathematics
Harvard University
Cambridge, MA 02138
USA
http://math.harvard.edu/~ssivek