On the homotopy type of the spaces of spherical knots in R-n

Abstract

We study the spaces of embeddings S-m hooked right arrow R-n and those of long embeddings R-m hooked right arrow 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-infinity -algebras of diagrams that encode their rational homotopy type when the codimension n- m is at least 3.