Upper bounds for the minimal number of singular fibers in a Lefschetz fibration over the torus

Noriyuki Hamada

doi:10.1307/mmj/1401973051

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arXiv · 1205.1111

Upper bounds for the minimal number of singular fibers in a Lefschetz fibration over the torus

Noriyuki Hamada

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Abstract

In this paper, we give some relations in the mapping class groups of oriented closed surfaces in the form that a product of a small number of right hand Dehn twists is equal to a single commutator. Consequently, we find upper bounds for the minimal number of singular fibers in a Lefschetz fibration over the torus.

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Noriyuki Hamada. 2012-05-05. Upper bounds for the minimal number of singular fibers in a Lefschetz fibration over the torus. https://doi.org/10.1307/mmj/1401973051

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