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Pseudo-Anosov elements of mapping class groups of Heegaard surfaces of the 3-sphere - MaRDI portal

Pseudo-Anosov elements of mapping class groups of Heegaard surfaces of the 3-sphere (Q534553)

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scientific article; zbMATH DE number 5895865
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Pseudo-Anosov elements of mapping class groups of Heegaard surfaces of the 3-sphere
scientific article; zbMATH DE number 5895865

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    Pseudo-Anosov elements of mapping class groups of Heegaard surfaces of the 3-sphere (English)
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    18 May 2011
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    Let \(H_g\) be the genus \(g\) handlebody with boundary \(\Sigma_g\) in the \(3\)-sphere obtained by attaching \(g\) \(1\)-handles to the \(3\)-ball. The restriction of a diffeomorphism of \(H_g\) to \(\Sigma_g\) gives a diffeomorphism of \(\Sigma_g\), allowing us to see the handlebody group of \(H_g\) as a subgroup of the mapping class group of \(\Sigma_g\). In the paper under review, an infinite family of pseudo-Anosov diffeomorphisms of \(H_g\) is constructed for \(g\geq 3\). For the proof that the constructed diffeomorphisms are pseudo-Anosov, a result of \textit{D. Margalit} and \textit{S. Spallone} [Math. Res. Lett. 14, No. 5-6, 853--863 (2007; Zbl 1163.57013)] is employed.
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    Heegaard surface
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    handlebody group
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    pseudo-Anosov diffeomorphism
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    mapping class group
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