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We produce simply-connected, minimal, symplectic Lefschetz fibrations realizing all the lattice points in the symplectic geography plane below the Noether line. This provides asymplecticextension of the classical works populating the complex geography plane with holomorphic Lefschetz fibrations. Our examples are obtained by rationally blowing down Lefschetz fibrations with clustered nodal fibers, the total spaces of which are potentially new homotopy elliptic surfaces. Similarly, clustering nodal fibers on higher genera Lefschetz fibrations on standard rational surfaces, we get rational blowdown configurations that yield new constructions of small symplectic exotic –manifolds. We present an example of a construction of a minimal symplectic exotic through this procedure applied to a genus– fibration.
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Lefschetz fibrations with arbitrary signature
We develop techniques to construct explicit symplectic Lefschetz fibrations over the2-sphere with any prescribed signature\sigmaand any spin type when\sigmais divisible by16. This solves a long-standing conjecture on the existence of such fibrations with positive signature. As applications, we produce symplectic4-manifolds that are homeomorphic but not diffeomorphic to connected sums ofS^2 \times S^2, with the smallest topology known to date, as well as larger examples as symplectic Lefschetz fibrations.
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- Award ID(s):
- 2005327
- PAR ID:
- 10562418
- Publisher / Repository:
- EMS Press
- Date Published:
- Journal Name:
- Journal of the European Mathematical Society
- Volume:
- 26
- Issue:
- 8
- ISSN:
- 1435-9855
- Page Range / eLocation ID:
- 2837 to 2895
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.4171/JEMS/1326
