On the homotopy type of the spaces of spherical knots in $R^n$

Victor Turchin; Thomas Willwacher

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arXiv · 2012.09965

On the homotopy type of the spaces of spherical knots in $R^n$

Victor Turchin·Thomas Willwacher

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Abstract

We study the spaces of embeddings $S^m\hookrightarrow R^n$ and those of long embeddings $R^m\hookrightarrow R^n$, i.e. embeddings of a fixed behavior outside a compact set. More precisely we look at the homotopy fiber of the inclusion of these spaces to the spaces of immersions. We find a natural fiber sequence relating these spaces. We also compare the $L_\infty$-algebras of diagrams that encode their rational homotopy type, when the codimension $n-m\geq 3$.

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Victor Turchin, Thomas Willwacher. 2020-12-17. On the homotopy type of the spaces of spherical knots in $R^n$. https://arxiv.org/abs/2012.09965

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