Dualizable tensor categories

Understand

We investigate the relationship between the algebra of tensor categories and the topology of framed 3-manifolds.

• On the one hand, tensor categories with certain algebraic properties determine topological invariants.
• We prove that fusion categories of nonzero global dimension are 3-dualizable, and therefore provide 3-dimensional 3-framed local field theories.
• We also show that all finite tensor categories are 2-dualizable, and yield categorified 2-dimensional 3-framed local field theories.