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Minimal number of singular fibers in a Lefschetz fibration
Author(s):
Mustafa
Korkmaz;
Burak
Ozbagci
Journal:
Proc. Amer. Math. Soc.
129
(2001),
1545-1549.
MSC (1991):
Primary 57M99;
Secondary 20F38
Posted:
October 20, 2000
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Abstract:
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.
References:
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- 1.
- J. Amoros, F. Bogomolov, L. Katzarkov, T. Pantev, (with an appendix by Ivan Smith), Symplectic Lefschetz fibrations with arbitrary fundamental groups, e-print: GT/9810042.
- 2.
- C. Cadavid, Ph.D. Dissertation, UT Austin, 1998.
- 3.
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- 10.
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- 11.
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- 12.
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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:
10.1090/S0002-9939-00-05676-8
PII:
S 0002-9939(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
Posted:
October 20, 2000
Communicated by:
Ronald A. Fintushel
Copyright of article:
Copyright
2000,
American Mathematical Society
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