Unknotting cones in the topological category
R. Richard Summerhill · Pacific Journal of Mathematics · 1972
Let Q be a topological g-manifold, let X be a compact metric space, and let bQ and aX denote the cones over Q and X, respectively.A proper embedding /: aX-> bQ (i.e., f(a) = b and f~ι[Q\ = X) is unknotted if there is homeomorphism h: bQ -> bQ such that hf -/, where / is the conical extension of /.In this paper it is proved that a proper embedding is unknotted if and only if bQ -f[aX] and bQ -f[ax] are of the same homotopy type and the embedding / satisfies a local flatness condition.