The mapping class groups of reducible Heegaard splittings of genus two

A 3-manifold which admits a genus- 2 reducible Heegaard splitting is one of the 3-sphere, \mathbb{S}^2 \times \mathbb{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....

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Bibliographic Details
Published in:Transactions of the American Mathematical Society 2019-02, Vol.371 (4), p.2473-2502
Main Authors: CHO, SANGBUM, KODA, YUYA
Format: Article
Language:English
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Summary:A 3-manifold which admits a genus- 2 reducible Heegaard splitting is one of the 3-sphere, \mathbb{S}^2 \times \mathbb{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.
ISSN:0002-9947
1088-6850
DOI:10.1090/tran/7375