Topological isotopy and Cochran's derived invariants

TL;DR

This paper constructs a non-PL link in 3-space with uncountably many isotopy classes and discusses properties of Cochran's invariants, revealing new insights into link isotopy and invariants.

Contribution

It introduces a novel example of a non-PL link with uncountably many isotopy classes and analyzes Cochran's invariants in this context.

Findings

Existence of a non-PL link not ambiently isotopic to any PL link.

Uncountably many I-equivalence classes of links.

Observations on Cochran's invariants β_i.

Abstract

We construct a link in the $3$-space that is not isotopic to any PL link (non-ambiently). In fact, there exist uncountably many $I$-equivalence classes of links. The paper also includes some observations on Cochran's invariants $\beta_i$.