Twisted book decompositions and the Goeritz groups

Daiki Iguchi; Yuya Koda

doi:10.1016/j.topol.2020.107064

Twisted book decompositions and the Goeritz groups

Daiki Iguchi, Yuya Koda

Research output: Contribution to journal › Article › peer-review

Abstract

We consider the Goeritz groups of the Heegaard splittings induced from twisted book decompositions. We show that there exist Heegaard splittings of distance 2 that have the infinite-order mapping class groups whereas that are not induced from open book decompositions. Explicit computation of those mapping class groups are given.

Original language	English
Article number	107064
Journal	Topology and its Applications
Volume	272
DOIs	https://doi.org/10.1016/j.topol.2020.107064
Publication status	Published - 2020 Mar 1
Externally published	Yes

Keywords

3-Manifold
Distance
Heegaard splitting
Mapping class group

ASJC Scopus subject areas

Geometry and Topology

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10.1016/j.topol.2020.107064

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title = "Twisted book decompositions and the Goeritz groups",

abstract = "We consider the Goeritz groups of the Heegaard splittings induced from twisted book decompositions. We show that there exist Heegaard splittings of distance 2 that have the infinite-order mapping class groups whereas that are not induced from open book decompositions. Explicit computation of those mapping class groups are given.",

keywords = "3-Manifold, Distance, Heegaard splitting, Mapping class group",

author = "Daiki Iguchi and Yuya Koda",

note = "Funding Information: The authors would like to thank the anonymous referee for his or her valuable comments and suggestions that helped them to improve the exposition. The second author is supported by JSPS KAKENHI Grant Numbers JP15H03620 , JP17K05254 , JP17H06463 , and JST CREST Grant Number JPMJCR17J4 . Publisher Copyright: {\textcopyright} 2020 Elsevier B.V.",

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AU - Iguchi, Daiki

AU - Koda, Yuya

N1 - Funding Information: The authors would like to thank the anonymous referee for his or her valuable comments and suggestions that helped them to improve the exposition. The second author is supported by JSPS KAKENHI Grant Numbers JP15H03620 , JP17K05254 , JP17H06463 , and JST CREST Grant Number JPMJCR17J4 . Publisher Copyright: © 2020 Elsevier B.V.

PY - 2020/3/1

Y1 - 2020/3/1

N2 - We consider the Goeritz groups of the Heegaard splittings induced from twisted book decompositions. We show that there exist Heegaard splittings of distance 2 that have the infinite-order mapping class groups whereas that are not induced from open book decompositions. Explicit computation of those mapping class groups are given.

AB - We consider the Goeritz groups of the Heegaard splittings induced from twisted book decompositions. We show that there exist Heegaard splittings of distance 2 that have the infinite-order mapping class groups whereas that are not induced from open book decompositions. Explicit computation of those mapping class groups are given.

KW - 3-Manifold

KW - Distance

KW - Heegaard splitting

KW - Mapping class group

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ER -

Twisted book decompositions and the Goeritz groups

Abstract

Keywords

ASJC Scopus subject areas

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