Non-looseness of boundaries of Legendrian ribbons

Kenneth L. Baker; Sinem Onaran

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arXiv · 2307.06828

Non-looseness of boundaries of Legendrian ribbons

Kenneth L. Baker·Sinem Onaran

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Abstract

Every null-homologous link in an oriented 3-manifold is isotopic to the boundary of a ribbon of a Legendrian graph for any overtwisted contact structure. However this is not the case if the boundary is required to be non-loose. Here, we define the `Tight Reattachment Property' for a Legendrian graph and show that it implies the boundary of its ribbon is non-loose. We also discuss the applicability of this property and examine examples and constructions of Legendrian graphs with this property.

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Kenneth L. Baker, Sinem Onaran. 2023-07-13. Non-looseness of boundaries of Legendrian ribbons. https://arxiv.org/abs/2307.06828

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