On the number of nested twice-punctured tori in a hyperbolic knot exterior (Q6545215)
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scientific article; zbMATH DE number 7854793
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the number of nested twice-punctured tori in a hyperbolic knot exterior |
scientific article; zbMATH DE number 7854793 |
Statements
On the number of nested twice-punctured tori in a hyperbolic knot exterior (English)
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29 May 2024
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JSJ decompositions are an important object and tool in 3-manifold topology. It is a natural question to ask for the number of JSJ pieces in the decomposition of a given 3-manifold along essential tori. For the case of Dehn surgery on a knot in \(S^{3}\), this is related to a bound for the number of pairwise disjoint, essential punctured tori in the knot complement. \N\NIn this paper, the authors show that there are at most six nonisotopic, nested, essential 2-holed tori in the complement of every hyperbolic knot in \(S^{3}\).
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incompressible surfaces in knot complements
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Seifert tori
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genus two handlebodies
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JSJ decompositions
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