Minimal number of singular fibers in a Lefschetz fibration

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2001-01-01

Author

Korkmaz, Mustafa

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There exists a (relatively minimal) genus g Lefschetz fibration with only one singular fiber over a closed (Riemann) surface of genus h iff g greater than or equal to 3 and h greater than or equal to 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.

Subject Keywords

Applied Mathematics, General Mathematics

URI

https://hdl.handle.net/11511/44403

Journal

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY

DOI

https://doi.org/10.1090/s0002-9939-00-05676-8

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Department of Mathematics, Article

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Citation Formats

M. Korkmaz, “Minimal number of singular fibers in a Lefschetz fibration,” PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, pp. 1545–1549, 2001, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/44403.