Minimal number of singular fibers in a Lefschetz fibration

Details Minimal number of singular fibers in a Lefschetz fibration Minimal number of singular fibers in a Lefschetz fibration

1998-12-08

arxiv.org/abs/math/9812051v3

Proc. Amer. Math. Soc. 129 (2001), 1545-1549

Mathematics

Geometric Topology

6 pages, 2 figures, second version

Scientific paper

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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