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

Sangbum Cho, Yuya Koda

研究成果: Article査読

8 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)4344-4371
ページ数28
ジャーナルInternational Mathematics Research Notices
2015
12
DOI
出版ステータスPublished - 2015
外部発表はい

ASJC Scopus subject areas

  • 数学一般

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