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Symplectic topology for 4-manifolds

Banff International Research Station for Mathematical Innovation and Discovery

Symplectic topology has been behind many advances in the study of the smooth topology of 4-manifolds. 4-manifolds which admit a symplectic structure give a nice subclass of smooth 4-manifolds where additional tools are available, while still exhibiting many of the exotic and topological phenomena occurring in generic smooth 4-manifolds. We will discuss some of the tools and major theorems that symplectic topology brings to the table. Instead of going into full technical detail, we will focus on the topological applications of these tools to understanding 4-manifolds and the surfaces they contain. We hope to discuss: adjunction formula and standard neighborhoods, using pseudoholomorphic curves to prove existence of certain surfaces or foliations by surfaces, positivity of intersections for uniqueness of surfaces and controlling isotopies, and symplectic branched coverings.

Mathematics; Manifolds And Cell Complexes

video/mp4

Author affiliation: University of California-Davis

2020-05-04

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/74267

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/