Lefschetz pencils and finitely presented groups

Ryoma Kobayashi, Naoyuki Monden

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

From the works of Gompf and Donaldson, it is known that every finitely presented group can be realized as the fundamental group of the total spaceof a Lefschetz pencil. We give an alternative proof of this fact by providing the monodromy explicitly. In the proof, we give an alternative construction of the monodromy of Gurtas' fibration and a lift of that to the mapping class group of a surface with two boundary components.

Original languageEnglish
Pages (from-to)359-388
Number of pages30
JournalPacific Journal of Mathematics
Volume282
Issue number2
DOIs
Publication statusPublished - Jun 1 2016
Externally publishedYes

Keywords

  • Fundamental group
  • Lefschetz fibration
  • Lefschetz pencil
  • Mapping class group

ASJC Scopus subject areas

  • Mathematics(all)

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