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A note on an example of Birman-Montesinos

Author: Takeshi Kaneto
Journal: Proc. Amer. Math. Soc. 83 (1981), 425-426
MSC: Primary 57N10
MathSciNet review: 624945
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Abstract: We will report the negative solution to a conjecture of Birman-Montesinos about their example of Heegaard diagram. This implies the negative answer to a question of Waldhausen related to minimal Heegaard splittings of $ 3$-manifolds.

References [Enhancements On Off] (What's this?)

  • [1] J. S. Birman and J. M. Montesinos, On minimal Heegaard splittings, Michigan Math. J. 27 (1980), 49-57. MR 555836 (81b:57007)
  • [2] F. Waldhausen, Heegaard-Zerlegungen der 3-Sphäre, Topology 7 (1968), 195-203. MR 0227992 (37:3576)
  • [3] -, Some problems on $ 3$-manifolds, Proc. Sympos. Pure Math., vol. 32, Amer. Math. Soc., Providence, R.I., 1978, pp. 313-322.

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Keywords: $ 3$-manifolds, minimal Heegaard splittings, pseudominimal Heegaard diagrams
Article copyright: © Copyright 1981 American Mathematical Society

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