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On page 6 of the article Symplectic Lefschetz fibrations with arbitrary fundamental groups, the authors state that for a Lefschetz fibration (with total space of dimension 4) the retraction of the regular fibre onto a critical fibre contains a vanishing cycle.

  • Why does such a vanishing cycle exist?
  • Is existence of vanishing cycles guaranteed when the total space has dimension higher than 4?
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