Small Lefschetz fibrations and exotic 4-manifolds

Date

2017-04-01

Author

Baykur, R. Inanc
Korkmaz, Mustafa

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We explicitly construct genus-2 Lefschetz fibrations whose total spaces are minimal symplectic 4-manifolds homeomorphic to complex rational surfaces CP2#pCP (CP) over bar (2) for P = 7,8,9, and to 3CP(2)#qCP (CP) over bar (2) for q = 12, . . . , 19. Complementarily, we prove that there are no minimal genus-2 Lefschetz fibrations whose total spaces are homeomorphic to any other simply-connected 4-manifold with b(+) <= 3, with one possible exception when b(+) = 3. Meanwhile, we produce positive Dehn twist factorizations for several new genus-2 Lefschetz fibrations with small number of critical points, including the smallest possible example, which follow from a reverse engineering procedure we introduce for this setting. We also derive exotic minimal symplectic 4-manifolds in the homeomorphism classes of CP2#4CP (CP) over bar (2) and 3CP(2)#6CP (CP) over bar (2) from small Lefschetz fibrations over surfaces of higher genera.

Subject Keywords

General Mathematics

URI

https://hdl.handle.net/11511/43270

Journal

MATHEMATISCHE ANNALEN

DOI

https://doi.org/10.1007/s00208-016-1466-2

Collections

Department of Mathematics, Article

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Citation Formats

R. I. Baykur and M. Korkmaz, “Small Lefschetz fibrations and exotic 4-manifolds,” MATHEMATISCHE ANNALEN, pp. 1333–1361, 2017, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/43270.