Lefschetz pencils and finitely presented groups

Ryoma Kobayashi; Naoyuki Monden

doi:10.2140/pjm.2016.282.359

Lefschetz pencils and finitely presented groups

Ryoma Kobayashi, Naoyuki Monden

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

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 language	English
Pages (from-to)	359-388
Number of pages	30
Journal	Pacific Journal of Mathematics
Volume	282
Issue number	2
DOIs	https://doi.org/10.2140/pjm.2016.282.359
Publication status	Published - Jun 1 2016
Externally published	Yes

Keywords

Fundamental group
Lefschetz fibration
Lefschetz pencil
Mapping class group

ASJC Scopus subject areas

Mathematics(all)

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10.2140/pjm.2016.282.359

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AU - Monden, Naoyuki

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N2 - 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.

AB - 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.

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KW - Mapping class group

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Lefschetz pencils and finitely presented groups

Abstract

Keywords

ASJC Scopus subject areas

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