Lefschetz Fibrations on 4-manifolds

Date

2009-01-01

Author

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 for , and to for . 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 , with one possible exception when . 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 and from small Lefschetz fibrations over surfaces of higher genera.

URI

https://hdl.handle.net/11511/86333

Relation

Handbook of Teichmuller Theory II

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Department of Mathematics, Book / Book chapter

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Citation Formats

M. Korkmaz, Lefschetz Fibrations on 4-manifolds. 2009, p. 296.