Work

From 3-dimensional skein theory to functions near ℚ

Year: 2025

Type: article

Abstract: Motivated by the Quantum Modularity Conjecture and its arithmetic aspects related to the Habiro ring of a number field, we define a map from the Kauffman bracket skein module of an integer homology 3-sphere to the Habiro ring, and use Witten’s conjecture (now a theorem) to show that the image is an effectively computable module of finite rank that can be used to phrase the quantum modularity conjecture.

Source: Annales de l’institut Fourier

DOI: 10.5802/aif.3740

Authors: Stavros Garoufalidis, Thang T. Q. Lê

Institutions: Southern University of Science and Technology, Georgia Institute of Technology

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: National Science Foundation

Awards: The Geometry and Topology of the Jones Polynomial, The Jones Polynomial and Hyperbolic Geometry of Surfaces