THE MAPPING CLASS GROUPS OF REDUCIBLE HEEGAARD SPLITTINGS OF GENUS TWO

Title
THE MAPPING CLASS GROUPS OF REDUCIBLE HEEGAARD SPLITTINGS OF GENUS TWO
Author
조상범
Keywords
GOERITZ GROUP; AUTOMORPHISMS; 3-SPHERE; PRESERVE
Issue Date
2019-02
Publisher
AMER MATHEMATICAL SOC
Citation
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, v. 371, NO 4, Page. 2473-2502
Abstract
A 3-manifold which admits a genus-2 reducible Heegaard splitting is one of the 3-sphere, S-2 x S-1, lens spaces and their connected sums. For each of those manifolds except most lens spaces, the mapping class group of the genus-2 splitting was shown to be finitely presented. In this work, we study the remaining generic lens spaces and show that the mapping class group of the genus-2 Heegaard splitting is finitely presented for any lens space by giving its explicit presentation. As an application, we show that the fundamental groups of the spaces of the genus-2 Heegaard splittings of lens spaces are all finitely presented.
URI
http://www.ams.org/journals/tran/2019-371-04/S0002-9947-2018-07375-5/http://repository.hanyang.ac.kr/handle/20.500.11754/108253
ISSN
0002-9947; 1088-6850
DOI
10.1090/tran/7375
Appears in Collections:
COLLEGE OF EDUCATION[S](사범대학) > MATHEMATICS EDUCATION(수학교육과) > Articles
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