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

DOI:
https://doi.org/10.1090/S0002-9939-00-05676-8

Published electronically:
October 20, 2000

MathSciNet review:
1713513

Full-text PDF

Abstract | References | Similar Articles | Additional Information

There exists a (relatively minimal) genus Lefschetz fibration with only one singular fiber over a closed (Riemann) surface of genus iff and . 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

Email:
korkmaz@math.metu.edu.tr

**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

Email:
bozbagci@math.uci.edu, bozbagci@math.msu.edu

DOI:
https://doi.org/10.1090/S0002-9939-00-05676-8

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