Knotted families from graspers

Pub Date : 2024-05-09 DOI:10.1112/topo.12337

Danica Kosanović

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Abstract

For any smooth manifold $M$ of dimension $d ⩾ 4$ , 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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对于维度为 d ⩾ 4 $d\geqslant 4$ 的任何光滑流形 M $M$，我们在弧或圆嵌入 M $M$的空间的同调群中，在每一个度数为 d - 3 $d-3$ 的倍数中构造了明确的类，并证明它们在古德威利和韦斯的泰勒塔中被检测到。这些类是从在 d $d$ 球中构造的弦链接族中获得的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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