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

Fingerprint

Finitely Presented Groups
Monodromy
Mapping Class Group
Alternatives
Fibration
Fundamental Group

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Lefschetz pencils and finitely presented groups. / Kobayashi, Ryoma; Monden, Naoyuki.

In: Pacific Journal of Mathematics, Vol. 282, No. 2, 01.06.2016, p. 359-388.

Research output: Contribution to journalArticle

Kobayashi, Ryoma ; Monden, Naoyuki. / Lefschetz pencils and finitely presented groups. In: Pacific Journal of Mathematics. 2016 ; Vol. 282, No. 2. pp. 359-388.
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