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Algebraic aspects of holomorphic quantum modular forms

Geometric Topology 2024-07-15 v2 High Energy Physics - Theory

Abstract

Matrix-valued holomorphic quantum modular forms are intricate objects that arise in successive refinements of the Volume Conjecture of knots and involve three holomorphic, asymptotic and arithmetic objects. It is expected that the algebraic properties of these objects can be deduced from the algebraic properties of descendant state integrals, and we illustrate this for the case of the (2,3,7)(-2,3,7)-pretzel knot.

Keywords

Cite

@article{arxiv.2403.02880,
  title  = {Algebraic aspects of holomorphic quantum modular forms},
  author = {Ni An and Stavros Garoufalidis and Shana Yunsheng Li},
  journal= {arXiv preprint arXiv:2403.02880},
  year   = {2024}
}

Comments

21 pages, 1 figure

R2 v1 2026-06-28T15:09:39.970Z