Morse structures on open books

David T. Gay; Joan E. Licata

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arXiv · 1508.05307

Morse structures on open books

David T. Gay·Joan E. Licata

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Abstract

We use parameterized Morse theory on the pages of an open book decomposition 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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David T. Gay, Joan E. Licata. 2015-08-21. Morse structures on open books. https://arxiv.org/abs/1508.05307

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