THE MAPPING CLASS GROUPS OF REDUCIBLE HEEGAARD SPLITTINGS OF GENUS TWO
- Authors
- Cho, Sangbum; Koda, Yuya
- Issue Date
- Feb-2019
- Publisher
- AMER MATHEMATICAL SOC
- Citation
- TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, v.371, no.4, pp.2473 - 2502
- Indexed
- SCIE
SCOPUS
- Journal Title
- TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
- Volume
- 371
- Number
- 4
- Start Page
- 2473
- End Page
- 2502
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/148398
- DOI
- 10.1090/tran/7375
- ISSN
- 0002-9947
- 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.
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