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Remarks on a Paper of M. Ochiai

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Abstract

This note is related to a nice short paper of M. Ochiai. We prove in a very fast way that the two-parameter family of Heegaard diagrams, constructed by Ochiai, encodes the genuine three-sphere. The result is obtained, up to isotopy, by using a sequence of only three moves in this order: a Whitehead–Zieschang reduction, a band sum and a cancellation of a handle.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Modena e Reggio Emilia, Via Campi 213/B, 41100, Modena, Italy

    Alberto Cavicchioli & Fulvia Spaggiari

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  1. Alberto Cavicchioli
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  2. Fulvia Spaggiari
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Correspondence to Alberto Cavicchioli.

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Cavicchioli, A., Spaggiari, F. Remarks on a Paper of M. Ochiai. manuscripta math. 120, 265–270 (2006). https://doi.org/10.1007/s00229-006-0009-7

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  • DOI: https://doi.org/10.1007/s00229-006-0009-7

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