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arXiv · 0911.1735

Connections between Floer-type invariants and Morse-type invariants of Legendrian knots

Michael Henry
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Abstract

We define an algebraic/combinatorial object on the front projection $Σ$ of a Legendrian knot called a Morse complex sequence, abbreviated MCS. This object is motivated by the theory of generating families and provides new connections between generating families, normal rulings, and augmentations of the Chekanov-Eliashberg DGA. In particular, we place an equivalence relation on the set of MCSs on $Σ$ and construct a surjective map from the equivalence classes to the set of chain homotopy classes of augmentations of $L_Σ$, where $L_Σ$ is the Ng resolution of $Σ$. In the case of Legendrian knot classes admitting representatives with two-bridge front projections, this map is bijective. We also exhibit two standard forms for MCSs and give explicit algorithms for finding these forms.

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BibTeXRIS

Michael Henry. 2010-09-15. Connections between Floer-type invariants and Morse-type invariants of Legendrian knots. https://doi.org/10.2140/pjm.2011.249.77

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