On the rational homotopy type of embedding spaces of manifolds in $R^n$

Benoit Fresse; Victor Turchin; Thomas Willwacher

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arXiv · 2008.08146

On the rational homotopy type of embedding spaces of manifolds in $R^n$

Benoit Fresse·Victor Turchin·Thomas Willwacher

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Abstract

We study the spaces of embeddings of manifolds in a Euclidean space. More precisely we look at the homotopy fiber of the inclusion of these spaces to the spaces of immersions. As a main result we express the rational homotopy type of connected components of those embedding spaces through combinatorially defined $L_\infty$-algebras of diagrams.

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Benoit Fresse, Victor Turchin, Thomas Willwacher. 2020-08-18. On the rational homotopy type of embedding spaces of manifolds in $R^n$. https://arxiv.org/abs/2008.08146

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