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Disk Complexes and Genus Two Heegaard Splittings for NonPrime 3-Manifolds

Title
Disk Complexes and Genus Two Heegaard Splittings for NonPrime 3-Manifolds
Author
조상범
Keywords
MAPPING CLASS-GROUPS; HAKEN SPHERES; LENS SPACES; 3-SPHERE; PRESERVE; HOMEOMORPHISMS; AUTOMORPHISMS; HANDLEBODY
Issue Date
2015-06
Publisher
OXFORD UNIV PRESS
Citation
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, NO 12, Page. 4344-4371
Abstract
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.
URI
https://academic.oup.com/imrn/article/2015/12/4344/675581/Disk-Complexes-and-Genus-Two-Heegaard-Splittingshttp://hdl.handle.net/20.500.11754/25878
ISSN
1073-7928; 1687-0247
DOI
10.1093/imrn/rnu061
Appears in Collections:
COLLEGE OF EDUCATION[S](사범대학) > MATHEMATICS EDUCATION(수학교육과) > Articles
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