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arXiv · 2307.14028

Knotted families from graspers

Danica Kosanović
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Abstract

For any smooth manifold $M$ of dimension $d\geq4$ we construct explicit classes in homotopy groups of spaces of embeddings of either an arc or a circle into $M$, in every degree that is a multiple of $d-3$, 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 $d$-ball.

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Danica Kosanović. 2023-07-26. Knotted families from graspers. https://doi.org/10.1112/topo.12337

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