Haefliger’s approach for spherical knots modulo immersions

IF 0.8 4区数学 Q2 MATHEMATICS Homology Homotopy and Applications Pub Date : 2023-10-04 DOI:10.4310/hha.2023.v25.n2.a4

Neeti Gauniyal

引用次数: 0

Abstract

$\def\Emb{\overline{Emb}}$We show that for the spaces of spherical embeddings modulo immersions $\Emb (S^n, S^{n+q})$ and long embeddings modulo immersions $\Emb_\partial (D^n, D^{n+q})$, the set of connected components is isomorphic to $\pi_{n+1} (SG, SG_q)$ for $q \geqslant 3$. As a consequence, we show that all the terms of the long exact sequence of the triad $(SG; SO, SG_q)$ have a geometric meaning relating to spherical embeddings and immersions.

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球节模浸的Haefliger方法

$\def\Emb{\overline{Emb}}$我们证明了对于球面嵌入模浸入$\Emb (S^n, S^{n+q})$和长嵌入模浸入$\Emb_\partial (D^n, D^{n+q})$的空间，对于$q \geqslant 3$，连通分量集同构于$\pi_{n+1} (SG, SG_q)$。因此，我们证明了三元组$(SG; SO, SG_q)$的长精确序列的所有项都具有与球面嵌入和浸入有关的几何意义。

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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来源期刊

Homology Homotopy and Applications 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Homology, Homotopy and Applications is a refereed journal which publishes high-quality papers in the general area of homotopy theory and algebraic topology, as well as applications of the ideas and results in this area. This means applications in the broadest possible sense, i.e. applications to other parts of mathematics such as number theory and algebraic geometry, as well as to areas outside of mathematics, such as computer science, physics, and statistics. Homotopy theory is also intended to be interpreted broadly, including algebraic K-theory, model categories, homotopy theory of varieties, etc. We particularly encourage innovative papers which point the way toward new applications of the subject.

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