Morse structures on open books

Gay, David; Licata, Joan

doi:10.1090/tran/7079

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. (to appear).
MathSciNet review: 3811509
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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 -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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