Uniform Convergence and Knot Equivalence

Forest Kobayashi

Uniform Convergence and Knot Equivalence

Geometric Topology 2021-01-12 v1

Authors: Forest Kobayashi

Abstract

Given a uniformly convergent sequence of ambient isotopies $(H_n)_{n\in\mathbb{N}}$ , bijectivity of the limit function $H_\infty$ together with a minor compactness condition guarantees that $H_\infty$ is also an ambient isotopy. By offloading the uniform convergence hypothesis to a more diagrammatic condition, we obtain sufficient conditions for performing countably-many Reidemeister moves. We use this to construct examples of tame knots with countably-many crossings and discuss what distinguishes these from similar-looking wild curves.

Keywords

knot theory periodic orbits in hamiltonian systems topological entropy

Cite

@article{arxiv.2101.04106,
  title  = {Uniform Convergence and Knot Equivalence},
  author = {Forest Kobayashi},
  journal= {arXiv preprint arXiv:2101.04106},
  year   = {2021}
}

Comments

34 pages, 44 figures

Uniform Convergence and Knot Equivalence

Abstract

Keywords

Cite

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