Semisimple higher categories

Theo Johnson-Freyd (Perimeter/Dalhousie)

26-Jul-2021, 19:00-20:00 (3 years ago)

Abstract: Semisimple higher categories are a quantum version of topological spaces (behaving sometimes like homotopy types and sometimes like manifolds) in which cells are attached along superpositions of other cells. Many operations from topology make sense for semisimple higher categories: they have homotopy sets (not groups), loop spaces, etc. For example, the extended operators in a topological sigma model form a semisimple higher category that can be thought of as a type of "cotangent bundle" of the target space. The "symplectic pairing" on this "cotangent bundle" is measured an S-matrix pairing aka Whitehead bracket defined on the homotopy sets of any (pointed connected) semisimple higher category, and the nondegeneracy of this pairing is a type of Poincare or Atiyah duality. This is joint work in progress with David Reutter.

differential geometrymetric geometry

Audience: researchers in the discipline


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