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

### Victor Turchin, Thomas Willwacher

Victor Turchin, Thomas Willwacher

**17/12/20**Published in : arXiv:2012.09965

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, assuming the codimension n-m\geq 3. 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.