Department of Mathematics

Geometry and Topology

  •  Chris Gerig, Harvard University
  •  Probing 4-manifolds with near-symplectic forms
  •  08/29/2019
  •  2:00 PM - 3:00 PM
  •  C304 Wells Hall

Most closed 4-manifolds do not admit symplectic forms, but most admit "near-symplectic forms", certain closed 2-forms which are symplectic outside of a collection of circles. This provides a gateway from the symplectic world to the non-symplectic world. I will first briefly sketch a geometric interpretation of the Seiberg-Witten invariants in terms of J-holomorphic curves that are compatible with the near-symplectic form. Although the Seiberg-Witten invariants don't apply to (potentially exotic) 4-spheres, nor do these spheres admit near-symplectic forms, there is still a way to bring in near-symplectic techniques.

 

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