TY - JOUR
T1 - Arc complexes, sphere complexes, and Goeritz groups
AU - Cho, Sangbum
AU - Koda, Yuya
AU - Seo, Arim
N1 - Funding Information:
The first-named author is supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Science, ICT and Future Planning (NRF-2015R1A1A1A05001071). The second-named author is supported by JSPS Postdoctoral Fellowships for Research Abroad, and by the Grant-in-Aid for Young Scientists (B), JSPS KAK-ENHI Grant Number 26800028.
Publisher Copyright:
© 2016, University of Michigan. All rights reserved.
PY - 2016/6
Y1 - 2016/6
N2 - 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.
AB - 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.
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U2 - 10.1307/mmj/1465329016
DO - 10.1307/mmj/1465329016
M3 - Article
AN - SCOPUS:84975853406
SN - 0026-2285
VL - 65
SP - 333
EP - 351
JO - Michigan Mathematical Journal
JF - Michigan Mathematical Journal
IS - 2
ER -