Monodromy Substitutions and Rational Blowdowns

Hisaaki Endo; Thomas E. Mark; Jeremy van Horn-Morris

doi:10.1112/jtopol/jtq041

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arXiv · 1004.3762

Monodromy Substitutions and Rational Blowdowns

Hisaaki Endo·Thomas E. Mark·Jeremy van Horn-Morris

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Abstract

We introduce several new families of relations in the mapping class groups of planar surfaces, each equating two products of right-handed Dehn twists. The interest of these relations lies in their geometric interpretation in terms of rational blowdowns of 4-manifolds, specifically via monodromy substitution in Lefschetz fibrations. The simplest example is the lantern relation, already shown by the first author and Gurtas to correspond to rational blowdown along a -4 sphere; here we give relations that extend that result to realize the "generalized" rational blowdowns of Fintushel-Stern and Park by monodromy subsitution, as well as several of the families of rational blowdowns discovered by Stipsicz-Szabó-Wahl.

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Hisaaki Endo, Thomas E. Mark, Jeremy van Horn-Morris. 2010-12-09. Monodromy Substitutions and Rational Blowdowns. https://doi.org/10.1112/jtopol%2Fjtq041

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