Morse structures on open books
Authors:
David T. Gay and Joan E. Licata
Journal:
Trans. Amer. Math. Soc. 370 (2018), 3771-3802
MSC (2010):
Primary 53D10; Secondary 57M27, 57M50
DOI:
https://doi.org/10.1090/tran/7079
Published electronically:
February 14, 2018
Corrigendum:
Trans. Amer. Math. Soc. 373 (2020), 3007-3008.
MathSciNet review:
3811509
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Abstract | References | Similar Articles | Additional Information
Abstract: We use parameterized Morse theory on the pages of an open book decomposition supporting a contact structure to efficiently encode the contact topology in terms of a labelled graph on a disjoint union of tori (one per binding component). This construction allows us to generalize the notion of the front projection of a Legendrian knot from the standard contact $\mathbb {R}^3$ to arbitrary closed contact $3$-manifolds. We describe a complete set of moves on such front diagrams, extending the standard Legendrian Reidemeister moves, and we give a combinatorial formula to compute the Thurston–Bennequin number of a nullhomologous Legendrian knot from its front projection.
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Additional Information
David T. Gay
Affiliation:
Department of Mathematics, Euclid Lab, University of Georgia, Athens, Georgia 30606
MR Author ID:
686652
Email:
d.gay@euclidlab.org
Joan E. Licata
Affiliation:
Mathematical Sciences Institute, The Australian National University, Canberra ACT0200, Australia
MR Author ID:
849641
Email:
joan.licata@anu.edu.au
Received by editor(s):
September 4, 2015
Received by editor(s) in revised form:
May 25, 2016, and August 1, 2016
Published electronically:
February 14, 2018
Additional Notes:
The first author was partially supported by NSF grant DMS-1207721.
Article copyright:
© Copyright 2018
American Mathematical Society
