Genus-3 Lefschetz Fibrations and Exotic 4-Manifolds with b(2)(+)=3

Date

2021-06-01

Author

Altunöz, Tülin

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We explicitly construct a genus-3 Lefschetz fibration over S-2, whose total space is T-2 x S-2 #6 (CP2) over bar using the monodromy of Matsumoto's genus-2 Lefschetz fibration. We then construct more genus-3 Lefschetz fibrations, whose total spaces are exotic minimal symplectic 4-manifolds 3CP(2)#q (CP2) over bar for q = 13,..., 19. We also generalize our construction to get genus-3k Lefschetz fibration structure on the 4-manifold Sigma(k) x S-2 #6 (CP2) over bar using the generalized Matsumoto's genus-2k Lefschetz fibration. From this generalized version, we derive further exotic 4-manifolds via Luttinger surgery and twisted fiber sum.

Subject Keywords

Symplectic 4-manifolds, Mapping class groups, Lefschetz fibrations, Lantern relation, Exotic manifolds

URI

https://hdl.handle.net/11511/90779

Journal

MEDITERRANEAN JOURNAL OF MATHEMATICS

DOI

https://doi.org/10.1007/s00009-021-01750-4

Collections

Department of Mathematics, Article

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Citation Formats

T. Altunöz, “Genus-3 Lefschetz Fibrations and Exotic 4-Manifolds with b(2)(+)=3,” MEDITERRANEAN JOURNAL OF MATHEMATICS, pp. 0–0, 2021, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/90779.