Growth of Turaev-Viro invariants and cabling

TL;DR

This paper proves that the Chen-Yang volume conjecture, relating Turaev-Viro invariants to simplicial volume, remains valid under specific cabling operations on 3-manifolds.

Contribution

It establishes the stability of the Chen-Yang conjecture under (2n+1,2)-cabling, extending its applicability to a broader class of 3-manifolds.

Findings

Chen-Yang conjecture is stable under (2n+1,2)-cabling

Growth rate of Turaev-Viro invariants determines simplicial volume

Extends the conjecture's validity to new manifold classes

Abstract

The Chen-Yang volume conjecture states that the growth rate of the Turaev-Viro invariants of a compact oriented $3$-manifold determines its simplicial volume. In this paper we prove that the Chen-Yang conjecture is stable under $(2n+1,2)$-cabling.