Arc Complexes, Sphere Complexes, and Goeritz Groupsopen access
- Authors
- Cho, Sangbum; Koda, Yuya; Seo, Arim
- Issue Date
- Jun-2016
- Publisher
- MICHIGAN MATHEMATICAL JOURNAL
- Citation
- MICHIGAN MATHEMATICAL JOURNAL, v.65, no.2, pp.333 - 351
- Indexed
- SCIE
SCOPUS
- Journal Title
- MICHIGAN MATHEMATICAL JOURNAL
- Volume
- 65
- Number
- 2
- Start Page
- 333
- End Page
- 351
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/154471
- DOI
- 10.1307/mmj/1465329016
- ISSN
- 0026-2285
- Abstract
- 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 S-2 x S-1, 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.
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