Lefschetz Fibrations and an Invariant of Finitely Presented Groups

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2009-01-01

Author

Korkmaz, Mustafa

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Every finitely presented group is the fundamental group of the total space of a Lefschetz fibration. This follows from results of Gompf and Donaldson, and was also proved by Amoros-Bogomolov-Katzarkov-Pantev. We give another proof by providing the monodromy explicitly. We then define the genus of a finitely presented group Gamma to be the minimal genus of a Lefschetz fibration with fundamental group Gamma. We also give some estimates of the genus of certain groups.

Subject Keywords

General Mathematics

URI

https://hdl.handle.net/11511/36975

Journal

INTERNATIONAL MATHEMATICS RESEARCH NOTICES

DOI

https://doi.org/10.1093/imrn/rnn164

Collections

Department of Mathematics, Article

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Citation Formats

M. Korkmaz, “Lefschetz Fibrations and an Invariant of Finitely Presented Groups,” INTERNATIONAL MATHEMATICS RESEARCH NOTICES, pp. 1547–1572, 2009, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/36975.