Minimal number of singular fibers in a Lefschetz fibration

Mustafa Korkmaz; Burak Ozbagci

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Minimal number of singular fibers in a Lefschetz fibration

Mustafa Korkmaz·Burak Ozbagci

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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>2 and h>1. 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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BibTeX RIS

Mustafa Korkmaz, Burak Ozbagci. 1999-02-22. Minimal number of singular fibers in a Lefschetz fibration. https://arxiv.org/abs/math/9812051

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