Small genus-4 Lefschetz fibrations on simply-connected 4-manifolds

Date

2022-03-07

Author

Altunöz, Tülin

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We consider simply connected 4-manifolds admitting Lefschetz fibrations over the 2-sphere. We explicitly construct nonhyperelliptic and hyperelliptic Lefschetz fibrations of genus 4 on simply-connected 4-manifolds which are exotic symplectic 4-manifolds in the homeomorphism classes of CP2 #8 and CP2#9, respectively. From these, we provide upper bounds for the minimal number of singular fibers of such fibrations. In addition, we prove that this number is equal to 18 for g = 3 when such fibrations are hyperelliptic. Moreover, we discuss these numbers for higher genera.

Subject Keywords

Symplectic 4-manifolds, mapping class groups, Lefschetz fibrations, exotic manifolds, SINGULAR FIBERS, MINIMAL NUMBER, SMOOTH STRUCTURES, SIGNATURE

URI

https://hdl.handle.net/11511/98994

Journal

TURKISH JOURNAL OF MATHEMATICS

DOI

https://doi.org/10.3906/mat-2108-85

Collections

Department of Mathematics, Article

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Citation Formats

T. Altunöz, “Small genus-4 Lefschetz fibrations on simply-connected 4-manifolds,” TURKISH JOURNAL OF MATHEMATICS, vol. 46, no. 4, pp. 1268–1290, 2022, Accessed: 00, 2022. [Online]. Available: https://hdl.handle.net/11511/98994.