Turaev-Viro invariants as an extended TQFT

TL;DR

This paper extends Turaev-Viro invariants to 3-manifolds with corners, forming an extended TQFT that is conjecturally equivalent to the Reshetikhin-Turaev TQFT associated with the Drinfeld center of the category.

Contribution

It introduces an extension of Turaev-Viro invariants to manifolds with corners, proposing a new extended TQFT framework linked to the Drinfeld center.

Findings

Partial proof of the conjectural equivalence between the extended Turaev-Viro TQFT and Reshetikhin-Turaev TQFT.

Extension of invariants to 3-manifolds with corners.

Establishment of a connection to the Drinfeld center of the spherical fusion category.

Abstract

In this paper we show how one can extend Turaev-Viro invariants, defined for an arbitrary spherical fusion category $C$, to 3-manifolds with corners. We demonstrate that this gives an extended TQFT which conjecturally coincides with the Reshetikhin-Turaev TQFT corresponding to the Drinfeld center $Z(C)$. In the present paper we give a partial proof of this statement.