Arc complexes, sphere complexes, and Goeritz groups

Sangbum Cho, Yuya Koda, Arim Seo

Research output: Contribution to journalArticlepeer-review


We show that if a Heegaard splitting is obtained by gluing a splitting of Hempel distance at least 4 and the genus-1 splitting of S2 × S1, then the Goeritz group of the splitting is finitely generated. To show this, we first provide a sufficient condition for a full subcomplex of the arc complex for a compact orientable surface to be contractible, which generalizes the result by Hatcher that the arc complexes are contractible. We then construct infinitely many Heegaard splittings, including the above-mentioned Heegaard splitting, for which suitably defined complexes of Haken spheres are contractible.

Original languageEnglish
Pages (from-to)333-351
Number of pages19
JournalMichigan Mathematical Journal
Issue number2
Publication statusPublished - 2016 Jun
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)


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