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Arc Complexes, Sphere Complexes, and Goeritz Groups

Title
Arc Complexes, Sphere Complexes, and Goeritz Groups
Author
조상범
Keywords
MAPPING CLASS-GROUPS; HEEGAARD-SPLITTINGS; CURVE COMPLEX; HAKEN SPHERES; LENS SPACES; 3-MANIFOLDS; AUTOMORPHISMS; SURFACES; 3-SPHERE; PRESERVE
Issue Date
2016-04
Publisher
MICHIGAN MATHEMATICAL JOURNAL
Citation
MICHIGAN MATHEMATICAL JOURNAL, v. 65, NO 2, Page. 333-351
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.
URI
https://arxiv.org/abs/1403.7832https://projecteuclid.org/euclid.mmj/1465329016http://hdl.handle.net/20.500.11754/52428
ISSN
0026-2285
Appears in Collections:
COLLEGE OF EDUCATION[S](사범대학) > MATHEMATICS EDUCATION(수학교육과) > Articles
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