Symplectic Lefschetz fibrations, rational blowdowns, and small exotic 4-manifolds

Geometry Topology Seminar
Monday, February 21, 2022 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 006
Jonathan Simone – Georgia Tech – jsimone7@gatech.edu
Jonathan Simone

Fiber sums and the rational blowdown have been very useful tools in constructing smooth, closed, oriented 4-manifolds. Applying these tools to genus g>1 Lefschetz fibrations with clustered nodal fibers, we will construct symplectic Lefschetz fibrations realizing all the lattice points in the symplectic geography plane below the Noether line, providing a symplectic extension of classical works populating the complex geography plane with holomorphic Lefschetz fibrations. Moreover, Lefschetz fibrations with certain clustered nodal fibers provide rational blowdown configurations that yield new constructions of small symplectic exotic 4-manifolds. We will present an example of a construction of a minimal symplectic exotic CP^2#-5CP^2 through this procedure applied to a genus-3 fibration. This work is joint with Inanc Baykur and Mustafa Korkmaz.