The mapping class group of a punctured surface is generated by three elements

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Let Mod (∑g,p) be the mapping class group of a closed oriented surface ∑g,p of genus g ≥1 with p punctures. Wajnryb proved that Mod(∑g,0) is generated by two elements. Korkmaz proved that one of these generators may be taken to be a Dehn twist. Korkmaz also proved the same result in the case of Mod(∑g,1). For p ≥ 2, we prove that Mod(∑g,p) is generated by three elements.

Original languageEnglish
Pages (from-to)1-9
Number of pages9
JournalHiroshima Mathematical Journal
Volume41
Issue number1
Publication statusPublished - Mar 1 2011
Externally publishedYes

Fingerprint

Dehn Twist
Mapping Class Group
Genus
Generator
Closed

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

Cite this

The mapping class group of a punctured surface is generated by three elements. / Monden, Naoyuki.

In: Hiroshima Mathematical Journal, Vol. 41, No. 1, 01.03.2011, p. 1-9.

Research output: Contribution to journalArticle

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