Lantern relations and rational blowdowns

Hisaaki Endo; Yusuf Z. Gurtas

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arXiv · 0808.0386

Lantern relations and rational blowdowns

Hisaaki Endo·Yusuf Z. Gurtas

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Abstract

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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Hisaaki Endo, Yusuf Z. Gurtas. 2008-08-04. Lantern relations and rational blowdowns. https://arxiv.org/abs/0808.0386

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