Knotted families from graspers
Geometric Topology
2025-10-08 v2 Algebraic Topology
Abstract
For any smooth manifold of dimension we construct explicit classes in homotopy groups of spaces of embeddings of either an arc or a circle into , in every degree that is a multiple of , and show that they are detected in the Taylor tower of Goodwillie and Weiss. The classes are obtained from families of string links constructed in the -ball.
Keywords
Cite
@article{arxiv.2307.14028,
title = {Knotted families from graspers},
author = {Danica Kosanović},
journal= {arXiv preprint arXiv:2307.14028},
year = {2025}
}
Comments
32 pages, 17 figures. v2: Shortened title, improved exposition, new figures, added a corollary about string links. Version accepted for publication in J. Topol