English

$Q$-Series and Quantum Spin Networks

Geometric Topology 2019-09-19 v3 General Topology

Abstract

The tail of a quantum spin network in the two-sphere is a qq-series associated to the network. We study the existence of the head and tail functions of quantum spin networks colored by 2n2n. We compute the qq-series for an infinite family of quantum spin networks and give the relation between the tail of these networks and the tail of the colored Jones polynomial. Finally, we show that the family of quantum spin networks under study satisfies a natural product structure, making these networks satisfy a natural product structure.

Cite

@article{arxiv.1810.01759,
  title  = {$Q$-Series and Quantum Spin Networks},
  author = {Mohamed Elhamdadi and Mustafa Hajij and Jesse S F Levitt},
  journal= {arXiv preprint arXiv:1810.01759},
  year   = {2019}
}

Comments

15 pages and 17 Figures

R2 v1 2026-06-23T04:27:14.948Z