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Let $X \hookrightarrow \mathbb R^d$ where $d$ is minimal (that is, $X \not \hookrightarrow \mathbb R^{d-1}$). When $X$ is the $(d-1)$-sphere, then the cone of $X$ still embeds into $\mathbb R^d$.

Are there any other manifolds $X$ which have this property?

(Related is Embeddability of the cone of Klein bottle to $\mathbb R^4$, where $X$ is the Klein Bottle)

  • What category are you working in: PL or topological? – Moishe Kohan Jul 18 '17 at 19:38
  • Triangulable manifolds, to be exact. PL is good too. Is there a difference between the two? –  Jul 19 '17 at 15:29
  • PL is not the same as triangulable. – Moishe Kohan Jul 21 '17 at 11:35
  • Right, but PL manifolds are a subset of triangulable ones. I meant to say that an answer to either class is fine, and the question in my comment asked if there was a difference (in the answer to this question) between PL and topological manifolds. –  Jul 23 '17 at 04:52

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