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Minimal number of singular fibers in a Lefschetz fibration

Authors: Mustafa Korkmaz and Burak Ozbagci
Journal: Proc. Amer. Math. Soc. 129 (2001), 1545-1549
MSC (1991): Primary 57M99; Secondary 20F38
Published electronically: October 20, 2000
MathSciNet review: 1713513
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Abstract | References | Similar Articles | Additional Information


There exists a (relatively minimal) genus $g$ Lefschetz fibration with only one singular fiber over a closed (Riemann) surface of genus $h$ iff $g \geq 3$ and $h \geq 2$. The singular fiber can be chosen to be reducible or irreducible. Other results are that every Dehn twist on a closed surface of genus at least three is a product of two commutators and no Dehn twist on any closed surface is equal to a single commutator.

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Additional Information

Mustafa Korkmaz
Affiliation: Department of Mathematics, Middle East Technical University, 06531 Ankara, Turkey

Burak Ozbagci
Affiliation: Department of Mathematics, University of California, Irvine, California 92697
Address at time of publication: Department of Mathematics, Michigan State University, Lansing, Michigan 48824

Keywords: Lefschetz fibrations, 4-manifolds, mapping class groups
Received by editor(s): February 26, 1999
Received by editor(s) in revised form: July 28, 1999
Published electronically: October 20, 2000
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2000 American Mathematical Society

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