Mathematics – Geometric Topology
Scientific paper
2010-04-21
Mathematics
Geometric Topology
28 pages, many figures. v2: minor edits; this version accepted for publication in Journal of Topology
Scientific paper
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-Szab\'o-Wahl.
Endo Hisaaki
Horn-Morris Jeremy Van
Mark Thomas E.
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