English

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 L2L^2-norm of SO(3)-knot states via geometric quantization capture the simplicial volume of knot complements.

Keywords

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}
}
R2 v1 2026-06-28T04:56:42.066Z