Morse structures on open books
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- by David T. Gay and Joan E. Licata PDF
- Trans. Amer. Math. Soc. 370 (2018), 3771-3802 Request permission
Corrigendum: Trans. Amer. Math. Soc. 373 (2020), 3007-3008.
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.References
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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.
- © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 370 (2018), 3771-3802
- MSC (2010): Primary 53D10; Secondary 57M27, 57M50
- DOI: https://doi.org/10.1090/tran/7079
- MathSciNet review: 3811509