Sequences of knots and their limits

TL;DR

This paper explores the concept of hyperfinite knots, which are limits of knot sequences under a specific invariant, and introduces new examples derived from sequences of torus knots.

Contribution

The paper provides novel examples of hyperfinite knots based on sequences of torus knots, expanding the understanding of their structure and properties.

Findings

New examples of hyperfinite knots from torus knot sequences

Extension of the concept of hyperfinite knots to specific knot sequences

Insights into the limits of knot invariants in metric spaces

Abstract

Hyperfinite knots, or limits of equivalence classes of knots induced by a knot invariant taking values in a metric space, were introduced in a previous article by the author. In this article, we present new examples of hyperfinite knots stemming from sequences of torus knots.