Singular fibers in Lefschetz fibrations on manifolds with b2+=1

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Abstract

We determine the minimal number of singular fibers of a nontrivial genus-g Lefschetz fibration X→S2 (with g≥14 or g≥6 and even) satisfying b2+(X)=1. Partial results for g odd with 9≤g≤13 are also discussed. Furthermore we prove a (weaker) lower bound for the number of singular fibers in a genus-g Lefschetz fibration in general.

Original languageEnglish
Pages (from-to)9-21
Number of pages13
JournalTopology and its Applications
Volume117
Issue number1
DOIs
Publication statusPublished - Jan 15 2002

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Keywords

  • 4-manifolds
  • Lefschetz fibrations
  • Vanishing cycles

ASJC Scopus subject areas

  • Geometry and Topology

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