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

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.

References in corpus (1)

• Commutators, Lefschetz fibrations and the signatures of surface bundles

Cited by in corpus (5)

• The Number of Singular Fibers in Hyperelliptic Lefschetz Fibrations
• Simple expressions for the holed torus relations
• Classification of genus-$1$ holomorphic Lefschetz pencils
• Small Lefschetz Fibrations on Simply-Connected $4$-Manifolds
• The existence of an indecomposable minimal genus two Lefschetz fibration