A necessary and sufficient condition for a 3-manifold to have genus \(g\) Heegaard splitting (a proof of Hass-Thompson conjecture) (Q1333599)
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scientific article; zbMATH DE number 639567
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A necessary and sufficient condition for a 3-manifold to have genus \(g\) Heegaard splitting (a proof of Hass-Thompson conjecture) |
scientific article; zbMATH DE number 639567 |
Statements
A necessary and sufficient condition for a 3-manifold to have genus \(g\) Heegaard splitting (a proof of Hass-Thompson conjecture) (English)
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17 October 1995
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The condition referred to in the title is that there exist a genus \(g\) handlebody in the manifold such that any knot in the manifold can be ambient isotoped to lie inside the handlebody. The genus 0 case was obtained by \textit{R. H. Bing} [Ann. Math., II. Ser. 68, 17-37 (1958; Zbl 0081.392)] and the genus 1 case by \textit{J. Hass} and \textit{A. Thompson} [Proc. Am. Math. Soc. 107, No. 4, 1107-1110 (1989; Zbl 0694.57006)].
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Heegard splitting
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genus
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3-manifold
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knot
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