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Abstract: We introduce several new families of relations in the mapping class groups ofplanar surfaces, each equating two products of right-handed Dehn twists. Theinterest of these relations lies in their geometric interpretation in terms ofrational blowdowns of 4-manifolds, specifically via monodromy substitution inLefschetz fibrations. The simplest example is the lantern relation, alreadyshown 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 monodromysubsitution, as well as several of the families of rational blowdownsdiscovered by Stipsicz-Szab\-o-Wahl.



Author: Hisaaki Endo, Thomas E. Mark, Jeremy van Horn-Morris

Source: https://arxiv.org/







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