A generalization of the Dijkgraaf-Witten invariants for cusped 3-manifolds

TL;DR

This paper extends Dijkgraaf-Witten invariants to cusped 3-manifolds, demonstrating their ability to distinguish certain hyperbolic 3-manifolds that share volume and other invariants.

Contribution

The authors generalize Dijkgraaf-Witten invariants for cusped 3-manifolds and show they can differentiate manifolds with identical volumes and Turaev-Viro invariants.

Findings

Generalized DW invariants distinguish some hyperbolic 3-manifolds with same volume.

Examples of manifolds with same volume and homology but different DW invariants.

Demonstrates the discriminative power of the generalized invariants.

Abstract

We introduce a generalization of the Dijkgraaf-Witten invariants for cusped or compact oriented 3-manifolds. We show that the generalized DW invariants distinguish some pairs of cusped hyperbolic 3-manifolds with the same hyperbolic volumes and with the same Turaev-Viro invariants. We also present an example of a pair of cusped hyperbolic 3-manifolds with the same hyperbolic volumes and with the same homology groups, whereas with distinct generalized DW invariants.