A manifestly Morita-invariant construction of Turaev–Viro invariants

Abstract: We present a bicategorical state sum construction for 3-manifold invariants. Using the pivotal bicategory of spherical module categories over a spherical fusion category, we construct invariants that manifestly preserve Morita equivalence. Our main result shows that this bicategorical invariant recovers the standard Turaev–Viro invariant, thereby proving Morita invariance of Turaev–Viro invariants without appealing to the Reshetikhin–Turaev construction.

This is joint work with Jürgen Fuchs, David Jaklitsch, and Christoph Schweigert.

mathematical physicsalgebraic topologycategory theoryquantum algebra

Audience: researchers in the topic

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