3D Quantum Trace Map: Construction and Applications in Ideally Triangulated 3-Manifolds

Explore the construction of the 3d quantum trace map in this 58-minute lecture by Sunghyuk Park from Harvard University. Delve into the recent joint work with Sam Panitch, which establishes a homomorphism between the Kauffman bracket skein module of an ideally triangulated 3-manifold and its (square root) quantum gluing module. Gain insights into the precise relationship between two quantizations of the character variety of ideally triangulated 3-manifolds. Examine the study of stated skein modules and their behavior under splitting, with a focus on face suspensions, which forms the foundation of this construction.