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.
Remarks on a paper of M. Ochiai / Cavicchioli, Alberto; Spaggiari, Fulvia. - In: MANUSCRIPTA MATHEMATICA. - ISSN 0025-2611. - STAMPA. - 120:(2006), pp. 265-270. [10.1007/s00229-006-0009-7]
Remarks on a paper of M. Ochiai
CAVICCHIOLI, Alberto;SPAGGIARI, Fulvia
2006
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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