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/https://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
- Files in This Item:
There are no files associated with this item.
- Export
- RIS (EndNote)
- XLS (Excel)
- XML