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arXiv · 2005.04173

On the Support Genus of Legendrian Knots

Sinem Onaran
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Abstract

In this paper, we show that any topological knot or link in $S^1 \times S^2$ sits on a planar page of an open book decomposition whose monodromy is a product of positive Dehn twists. As a consequence, any knot or link type in $S^1 \times S^2$ has a Legendrian representative having support genus zero. We also show this holds for some knots and links in the lens spaces $L(p,1)$.

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Sinem Onaran. 2020-05-08. On the Support Genus of Legendrian Knots. https://arxiv.org/abs/2005.04173

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