The mapping class groups of reducible heegaard splittings of genus two

Sangbum Cho, Yuya Koda

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

A 3-manifold which admits a genus-2 reducible Heegaard splitting is one of the 3-sphere, S 2 × 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.

Original languageEnglish
Pages (from-to)2473-2502
Number of pages30
JournalTransactions of the American Mathematical Society
Volume371
Issue number4
DOIs
StatePublished - 2019

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