Disk complexes and genus two Heegaard splittings for nonprime 3-manifolds

Sangbum Cho, Yuya Koda

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

Abstract

Given a genus two Heegaard splitting for a nonprime 3-manifold, we define a special subcomplex of the disk complex for one of the handlebodies of the splitting, and then show that it is contractible. As applications, first we show that the complex of Haken spheres for the splitting is contractible, which refines the results of Lei and Lei-Zhang. Secondly, we classify all the genus two Heegaard splittings for nonprime 3-manifolds, which is a generalization of the result of Montesinos-Safont. Finally, we show that the mapping class group of the splitting, called the Goeritz group, is finitely presented by giving its explicit presentation.

Original languageEnglish
Pages (from-to)4344-4371
Number of pages28
JournalInternational Mathematics Research Notices
Volume2015
Issue number12
DOIs
Publication statusPublished - 2015
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics

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