2021/08/24 by Sanjay Kumar, Kumar, Sanjay, Joseph M. Melby +1 · 1 citation
Mathematics · #57K14 #57K16 #57K31 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2108.10466
openalex publication_date 2021/08/24 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
In this paper, we show that the Turaev-Viro invariant volume conjecture posed by Chen and Yang is preserved under gluings of toroidal boundary components for a family of 3-manifolds. In particular, we show that the asymptotics of the Turaev-Viro invariants are additive under certain gluings of elementary pieces arising from a construction of hyperbolic cusped 3-manifolds due to Agol. The gluings of the elementary pieces are known to be additive with respect to the simplicial volume. This allows us to construct families of manifolds with an arbitrary number of hyperbolic pieces such that the resultant manifolds satisfy an extended version of the Turaev-Viro invariant volume conjecture.