Frobenius-Schur Indicators and the Mapping Class Group of the Torus

Abstract

The Turaev-Viro state sum invariant can be extended to 3-manifolds with free boundaries. We use this fact to describe generalized Frobenius-Schur indicators as Turaev-Viro invariants of solid tori. This provides a geometric understanding of the $\mathrm{SL}(2,\mathbb{Z})$-equivariance of these indicators.

29 pages

References in corpus (2)

• Turaev-Viro invariants as an extended TQFT
• Matrix product operator symmetries and intertwiners in string-nets with domain walls

Cited by in corpus (1)

• A geometrical description of untwisted 3d Dijkgraaf-Witten TQFT with defects