Link homotopic but not isotopic
Bakul Sathaye

TL;DR
This paper constructs examples of links in 3-sphere that are link homotopic but not link isotopic, with all proper sublinks isotopic to a given link, and explores properties related to Milnor invariants.
Contribution
It introduces a method to produce links that are link homotopic but not isotopic, extending understanding of link equivalence relations.
Findings
Existence of links link homotopic but not isotopic to a given link.
Proper sublinks are all isotopic to the original link.
Construction of links with zero Milnor invariants when starting from an unlink.
Abstract
Given an -component link in (), we construct a family of links which are link homotopic, but not link isotopic, to . Every proper sublink of such a link is link isotopic to the corresponding sublink of . Moreover, if is an unlink then there exist links that in addition to the above properties have all Milnor invariants zero.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Algebraic Geometry and Number Theory
