English

Infinitely many knots with non-integral trace

Geometric Topology 2020-09-29 v2

Abstract

We prove that there are infinitely many non-homeomorphic hyperbolic knot complements S3Ki=H3/ΓiS^3\setminus K_i = \mathbb{H}^3/\Gamma_i for which Γi\Gamma_i contains elements whose trace is an algebraic non-integer.

Keywords

Cite

@article{arxiv.2009.01481,
  title  = {Infinitely many knots with non-integral trace},
  author = {Alan W. Reid and Nicholas Rouse},
  journal= {arXiv preprint arXiv:2009.01481},
  year   = {2020}
}

Comments

15 pages, 6 figures; v2 includes answers to some questions in section 8 raised in v1

R2 v1 2026-06-23T18:17:10.201Z