Haefliger's approach for spherical knots modulo immersions

Abstract

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

24 pages