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Lefschetz Fibrations and an Invariant of Finitely Presented Groups
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Date
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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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.