Lefschetz fibrations on cotangent bundles and some plumbings

• Sangjin Lee ^[1]
  1. [1] Korea Institute for Advanced Study

     Korea Institute for Advanced Study

     Corea del Sur

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 31, Nº. 5, 2025
• Idioma: inglés
• DOI: 10.1007/s00029-025-01089-8
• Enlaces
  • Texto completo
• Resumen

  • Lefschetz fibrations are powerful tools in studying symplectic topology. The following are a few examples of that: When a Lefschetz fibration is given, one can define the Fukaya-Seidel category as described in [24]. In [2, 17, 18], the authors used Lefschetz fibrations for constructing diffeomorphic pairs of different Weinstein manifolds. When Wu [27] studied the symplectic mapping class group of the Milnor fiber of An-type, the well-known Lefschetz fibration of the Milnor fiber played a key role. McLean [20, 21] showed that one could compute a symplectic homology of a Liouville manifold from a Lefschetz fibration and its monodromy map. It is natural to ask which symplectic manifolds admit Lefschetz fibrations. Giroux and Pardon [14] gave a wonderful answer. They proved that every Stein manifold should admit a Lefschetz fibration. Moreover, [14] proved that every Weinstein manifold should admit a Lefschetz fibration indirectly, based on the equivalence between Stein and Weinstein manifolds.

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