Lantern relations and rational blowdowns

Details Lantern relations and rational blowdowns Lantern relations and rational blowdowns

2008-08-04

arxiv.org/abs/0808.0386v1

Mathematics

Geometric Topology

10 pages, 7 figures

Scientific paper

We discuss a connection between the lantern relation in mapping class groups and the rational blowing down process for 4-manifolds. More precisely, if we change a positive relator in Dehn twist generators of the mapping class group by using a lantern relation, the corresponding Lefschetz fibration changes into its rational blowdown along a copy of the configuration C_2. We exhibit examples of such rational blowdowns of Lefschetz fibrations whose blowup is homeomorphic but not diffeomorphic to the original fibration.

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