SO(3)-Knot States and the Volume Conjecture
Mathematical Physics
2022-11-02 v1 Geometric Topology
math.MP
Abstract
We study the alternating subspace of holomorphic sections of a special prequantum line bundle over SU(2)-character variety of torus, and show that it is isomorphic to the projective representation of mapping class group of peripheral torus given by the SO(3) Witten-Chern-Simons theory. We conjecture that the large r asymptotics of -norm of SO(3)-knot states via geometric quantization capture the simplicial volume of knot complements.
Cite
@article{arxiv.2211.00570,
title = {SO(3)-Knot States and the Volume Conjecture},
author = {Honghuai Fang},
journal= {arXiv preprint arXiv:2211.00570},
year = {2022}
}