紀要論文

紀要論文

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Osaka Journal of Mathematics. 2020, 57(1), p. 103-140

GENERALIZED HEEGAARD SPLITTINGS AND THE DISK COMPLEX

Kim, Jungsoo

Osaka University and Osaka City University, Departments of Mathematics

英語

text

2020-01

Let M be an orientable, irreducible 3-manifold and (V,W;F) a weakly reducible, unstabilized Heegaard splitting of M of genus at least three. In this article, we define an equivalence relation ~ on the set of the generalized Heegaard splittings obtained by weak reductions and find special subsets of the disk complex D(F) named by the “equivalent clusters”, where we can find a canonical function Φ from the set of equivalent clusters to the set of the equivalent classes for the relation ∼. These equivalent classes are more detailed than the isotopy classes of the generalized Heegaard splittings obtained by weak reductions from F. In the last section, we prove Φ is a bijection if the genus of F is three.

10.18910/73740

73740

GENERALIZED HEEGAARD SPLITTINGS AND THE DISK COMPLEX

Kim, Jungsoo

Osaka University and Osaka City University, Departments of Mathematics

英語

2020-01

Osaka Journal of Mathematics

57

1

103

140

https://hdl.handle.net/11094/73740

10.18910/73740

https://doi.org/10.18910/73740