3d quantum trace map
Abstract
We construct the 3d quantum trace map, a homomorphism from the Kauffman bracket skein module of an ideally triangulated 3-manifold to its (square root) quantum gluing module, thereby giving a precise relationship between the two quantizations of the character variety of ideally triangulated 3-manifolds.This map, whose existence was conjectured earlier by Agarwal, Gang, Lee, Romo (2022), is a natural 3-dimensional analog of the 2d quantum trace map of Bonahon and Wong (2011).Our construction is based on the study of stated skein modules and their behavior under splitting, especially into face suspensions.1. Introduction 2255 2. Classical story 2258 3. Stated skein modules of 3-manifolds 2264 4. Structure theorems for 3-balls 2287 5.Quantum trace map for triangulated 3-manifolds 2295 6.
Fields of Study & Subjects
Quantum Computing Algorithms and Architecture
Publication details
- Journal / source
- Algebraic & Geometric Topology
- Publisher
- Mathematical Sciences Publishers
- Volume
- 26
- Issue
- 6
- Pages
- 2255–2314
- Publication date
- 22 June 2026
- Language
- EN