paper

SO(3)-Knot States and the Volume Conjecture

arXiv:2211.00570

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.

SO(3)-Knot States and the Volume Conjecture · wovepaper