Symplectic trisections and the adjunction inequality

Symplectic trisections and the adjunction inequality

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Peter Lambert-Cole, University of Georgia

Zoom link:  https://princeton.zoom.us/j/453512481?pwd=OHZ5TUJvK2trVVlUVmJLZkhIRHFDUT09

The minimal genus problem is a fundamental question in smooth 4-manifold topology. Every 2-dimensional homology class can be represented by a surface. But how small can this surface be? A generation ago, techniques from gauge theory were used to solve this in a large class of 4-manifolds with extra geometric structure, namely symplectic 4-manifolds. Recent work on trisections if 4-manifolds has revealed an deep connection with symplectic geometry and gives a new perspective on this result.