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GENERALIZED HEEGAARD SPLITTINGS AND THE DISK COMPLEX

Kim, Jungsoo 大阪大学 DOI:10.18910/73740

2020.01

概要

Let M be an orientable, irreducible 3-manifold and (, ; 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 (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. ...

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参考文献

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BK21 PLUS SNU Mathematical Sciences Division

Seoul National University

1 Gwanak-ro, Gwanak-gu, Seoul 08826

Republic of Korea

[Current Address:]

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147, Dong-gu Office Street, Dong-gu

Daejeon 34691

Republic of Korea

e-mail: pibonazi@gmail.com

...

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