Lantern relations and rational blowdowns

2008/08/04 by Hisaaki Endo, Endo, Hisaaki, Yusuf Z. Gürtaş +1 · 3 citations
Mathematics · #57N13 #57R17 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.0808.0386

openalex publication_date 2008/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 C₂. We exhibit examples of such rational blowdowns of Lefschetz fibrations whose blowup is homeomorphic but not diffeomorphic to the original fibration.

Citations

• Elliptic surfaces without 1-handles

Cited by

• A note on the topology of Lefschetz fibrations
• Lefschetz pencils on a complex projective plane from a topological viewpoint
• Orientation double covers of non-orientable Lefschetz fibrations

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