Connected Primitive Disk Complexes and Genus Two Goeritz Groups of Lens Spaces

Title
Connected Primitive Disk Complexes and Genus Two Goeritz Groups of Lens Spaces
Author
조상범
Keywords
HEEGAARD-SPLITTINGS; AUTOMORPHISMS; 3-SPHERE; PRESERVE; HANDLEBODY
Issue Date
2016-12
Publisher
OXFORD UNIV PRESS
Citation
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, NO 23, Page. 7302-7340
Abstract
Given a stabilized Heegaard splitting of a three-manifold, the primitive disk complex for the splitting is the subcomplex of the disk complex for a handlebody in the splitting spanned by the vertices of the primitive disks. In this work, we study the structure of the primitive disk complex for the genus-2 Heegaard splitting of each lens space. In particular, we show that the complex for the genus-2 splitting for the lens space L(p, q) with 1 ˂= q ˂= p/2 is connected if and only if p = +/- 1 (mod q), and describe the combinatorial structure of each of those complexes. As an application, we obtain a finite presentation of the genus-2 Goeritz group of each of those lens spaces, the group of isotopy classes of orientation preserving homeomorphisms of the lens space that preserve the genus-2 Heegaard splitting of it.
URI
https://academic.oup.com/imrn/article/2016/23/7302/2633481http://repository.hanyang.ac.kr/handle/20.500.11754/103101
ISSN
1073-7928; 1687-0247
DOI
10.1093/imrn/rnv399
Appears in Collections:
COLLEGE OF EDUCATION[S](사범대학) > MATHEMATICS EDUCATION(수학교육과) > Articles
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