Lefschetz fibrations with arbitrary signature

  • R. İnanç Baykur

    University of Massachusetts, Amherst, USA
  • Noriyuki Hamada

    University of Massachusetts, Amherst, USA
Lefschetz fibrations with arbitrary signature cover
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Abstract

We develop techniques to construct explicit symplectic Lefschetz fibrations over the -sphere with any prescribed signature and any spin type when is divisible by . This solves a long-standing conjecture on the existence of such fibrations with positive signature. As applications, we produce symplectic -manifolds that are homeomorphic but not diffeomorphic to connected sums of , with the smallest topology known to date, as well as larger examples as symplectic Lefschetz fibrations.

Cite this article

R. İnanç Baykur, Noriyuki Hamada, Lefschetz fibrations with arbitrary signature. J. Eur. Math. Soc. 26 (2024), no. 8, pp. 2837–2895

DOI 10.4171/JEMS/1326