Invariants of Legendrian and transverse knots in monopole knot homology

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Title: Invariants of Legendrian and transverse knots in monopole knot homology
Authors: Baldwin, JA
Sivek, S
Item Type: Working Paper
Abstract: We use the contact invariant defined in [2] to construct a new invariant of Legendrian knots in Kronheimer and Mrowka's monopole knot homology theory (KHM), following a prescription of Stipsicz and V\'ertesi. Our Legendrian invariant improves upon an earlier Legendrian invariant in KHM defined by the second author in several important respects. Most notably, ours is preserved by negative stabilization. This fact enables us to define a transverse knot invariant in KHM via Legendrian approximation. It also makes our invariant a more likely candidate for the monopole Floer analogue of the "LOSS" invariant in knot Floer homology. Like its predecessor, our Legendrian invariant behaves functorially with respect to Lagrangian concordance. We show how this fact can be used to compute our invariant in several examples. As a byproduct of our investigations, we provide the first infinite family of nonreversible Lagrangian concordances between prime knots.
Issue Date: 11-Feb-2019
URI: http://hdl.handle.net/10044/1/52048
Copyright Statement: © 2014 The Authors
Keywords: math.SG
math.GT
Notes: 28 pages, 7 figures; this paper was originally part of arXiv:1403.1930
Appears in Collections:Pure Mathematics
Mathematics
Faculty of Natural Sciences



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