Torus-covering knot groups and their irreducible metabelian $SU(2)$-representations

Inasa Nakamura

doi:10.4310/AJM.250717205430

Torus-covering knot groups and their irreducible metabelian $SU(2)$-representations

Geometric Topology 2025-07-21 v3

Authors: Inasa Nakamura

View on arXiv ↗ PDF ↗ DOI ↗

Abstract

A torus-covering $T^2$ -knot is a surface-knot of genus one determined from a pair of commutative braids. For a torus-covering $T^2$ -knot $F$ , we determine the number of irreducible metabelian $SU(2)$ -representations of the knot group of $F$ in terms of the knot determinant of $F$ . It is similar to the result due to Lin for the knot group of a classical knot. Further, we investigate the number of irreducible metabelian $SU(2)$ -representations using Fox's $p$ -colorability.

Keywords

torus-covering knot knot group metabelian su(2)-representation knot determinant fox p-colorability

Cite

@article{arxiv.1909.13526,
  title  = {Torus-covering knot groups and their irreducible metabelian $SU(2)$-representations},
  author = {Inasa Nakamura},
  journal= {arXiv preprint arXiv:1909.13526},
  year   = {2025}
}

Comments

26 pages, 3 figures, minor revision, to appear in Asian J. Math

Torus-covering knot groups and their irreducible metabelian $SU(2)$-representations

Abstract

Keywords

Cite

Comments

Related papers