Knotted solid tori in contact manifolds

In this note we study solid tori in contact manifolds. Specifically, we study the width of a knot type and give criteria for when it is equal to the maximal Thurston-Bennequin invariant, and when it is larger. We also prove there are many ``non-thickenable" tori in many knot types. These had previously only been observed in $S^3$.

Publication Details

Journal
ArXiv.org
Published
2025-02-21
Primary Topic
Geometric and Algebraic Topology
Type
article
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article

Knotted solid tori in contact manifolds

ArXiv.org
Geometric and Algebraic Topology
article

Knotted solid tori in contact manifolds

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Abstract

In this note we study solid tori in contact manifolds. Specifically, we study the width of a knot type and give criteria for when it is equal to the maximal Thurston-Bennequin invariant, and when it is larger. We also prove there are many ``non-thickenable" tori in many knot types. These had previously only been observed in $S^3$.

ArXiv.org
Openalex Percentile: Top 41%
Geometric and Algebraic Topology
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Knotted solid tori in contact manifolds · ArXiv.org (2025) | TGRS Research Map | TGRS