Mapping class group of a plane curve germ

David Marín; Jean François Mattei

doi:https://doi.org/10.1016/j.topol.2011.04.009

Mapping class group of a plane curve germ

David Marín, Jean François Mattei

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

5 Citations (Scopus)

Abstract

We prove that every topological conjugacy between two germs of singular holomorphic curves in the complex plane is homotopic to another conjugacy which extends homeomorphically to the exceptional divisors of their minimal desingularisations. As an application we give an explicit presentation of a finite index subgroup of the mapping class group of the germ of such a singularity. © 2011 Elsevier B.V.

Original language	English
Pages (from-to)	1271-1295
Journal	Topology and its Applications
Volume	158
DOIs	https://doi.org/10.1016/j.topol.2011.04.009
Publication status	Published - 1 Jul 2011

Keywords

Mapping class group
Plane curve singularities

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https://doi.org/10.1016/j.topol.2011.04.009

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title = "Mapping class group of a plane curve germ",

abstract = "We prove that every topological conjugacy between two germs of singular holomorphic curves in the complex plane is homotopic to another conjugacy which extends homeomorphically to the exceptional divisors of their minimal desingularisations. As an application we give an explicit presentation of a finite index subgroup of the mapping class group of the germ of such a singularity. {\textcopyright} 2011 Elsevier B.V.",

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author = "David Mar{\'i}n and Mattei, {Jean Fran{\c c}ois}",

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AU - Mattei, Jean François

PY - 2011/7/1

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N2 - We prove that every topological conjugacy between two germs of singular holomorphic curves in the complex plane is homotopic to another conjugacy which extends homeomorphically to the exceptional divisors of their minimal desingularisations. As an application we give an explicit presentation of a finite index subgroup of the mapping class group of the germ of such a singularity. © 2011 Elsevier B.V.

AB - We prove that every topological conjugacy between two germs of singular holomorphic curves in the complex plane is homotopic to another conjugacy which extends homeomorphically to the exceptional divisors of their minimal desingularisations. As an application we give an explicit presentation of a finite index subgroup of the mapping class group of the germ of such a singularity. © 2011 Elsevier B.V.

KW - Mapping class group

KW - Plane curve singularities

U2 - https://doi.org/10.1016/j.topol.2011.04.009

DO - https://doi.org/10.1016/j.topol.2011.04.009

M3 - Article

SN - 0166-8641

VL - 158

SP - 1271

EP - 1295

JO - Topology and its Applications

JF - Topology and its Applications

ER -

Mapping class group of a plane curve germ

Abstract

Keywords

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