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arxiv: math/9812051 · v3 · submitted 1998-12-08 · 🧮 math.GT · math.SG

Minimal number of singular fibers in a Lefschetz fibration

classification 🧮 math.GT math.SG
keywords closedgenussingularsurfacedehnfiberfibrationlefschetz
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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>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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