Minimality and fiber sum decompositions of Lefschetz fibrations

2014/07/21 by R. Inanc Baykur, Baykur, R. Inanc
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Symplectic Geometry (math.SG) #math.GT #math.SG

paper · pdf · doi:10.48550/arxiv.1407.5351

10 pages. Final questions are updated

arxiv created 2015/08/26 · arxiv updated 2015/08/27

Abstract

We give a short proof of a conjecture of Stipsicz on the minimality of fiber sums of Lefschetz fibrations, which was proved earlier by Usher. We then construct the first examples of genus g > 1 Lefschetz fibrations on minimal symplectic 4-manifolds which, up to diffeomorphisms of the summands, admit unique decompositions as fiber sums.

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