Department of Mathematics

Topology

  •  Counting associatives and Seiberg-Witten equations
  •  10/02/2017
  •  4:10 PM - 5:30 PM
  •  C304 Wells Hall
  •  Thomas Walpuski, MSU

There is a natural functional on the space of orientation 3-dimensional submanifolds in a G2-manifold. Its critical points are associative submanifolds, a special class of volume-minimizing submanifolds which obey an elliptic deformation theory. Given this, it is a natural question whether one can count associative submanifolds in order to construct an enumerative invariant for G2–manifolds. I will explain several geometric scenarios, which prohibit a naive count of such submanifolds cannot possible be invariant. I will then go on to discuss how (generalized) Seiberg-Witten equations might help cure these problems.

 

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Department of Mathematics
Michigan State University
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