Topological isotopy and Cochran's derived invariants

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 ${\beta }_i$.

18 pages, 11 figures. To appear in "Topology, Geometry, and Dynamics: Rokhlin Memorial" (St.-Petersburg, August 19-23, 2019), Contemporary Mathematics, 772 (V. M. Buchstaber, A. V. Malyutin, T. E. Panov, A. M. Vershik, eds.), Amer. Math. Soc., Providence, RI, 2021