## Minimal number of singular fibers in a Lefschetz fibration

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- by Mustafa Korkmaz and Burak Ozbagci PDF
- Proc. Amer. Math. Soc.
**129**(2001), 1545-1549 Request permission

## Abstract:

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.## References

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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
- MR Author ID: 643774
- ORCID: 0000-0002-9758-1045
- Email: bozbagci@math.uci.edu, bozbagci@math.msu.edu
- 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
- © Copyright 2000 American Mathematical Society
- 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
- MathSciNet review: 1713513