Vol. 40, No. 1, 1972

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Unknotting cones in the topological category

Ralph Richard Summerhill

Vol. 40 (1972), No. 1, 221–228

Let Q be a topological q-manifold, let X be a compact metric space, and let bQ and aX denote the cones over Q and X, respectively. A proper embedding f : aX bQ (i.e., f(a) = b and f1[Q] = X) is unknotted if there is homeomorphism h : bQ bQ such that hf = f, where f is the conical extension of f. 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 f satisfies a local flatness condition.

Mathematical Subject Classification
Primary: 57A35
Received: 13 August 1970
Revised: 24 November 1970
Published: 1 January 1972
Ralph Richard Summerhill