Is there an $m$-dimensional simplicial complex $S$ with the following properties:

*The cone over $S$ is homeomorphic to $\mathbb{E}^{m+1}$.*Here $\mathbb{E}^{m+1}$ denoes the $(m+1)$-dimensional Euclidean space.*There is a vertex $v$ in $S$ such that the complement $S\backslash\{v\}$ is not simply connected.*

**Comments.**

If such example exist, the cone over $v$ has to from a wild half-line in the Euclidean space. It has to be an embedding of $[0,\infty)$ which complement is not simply connected.

The first condition is equivalent to the following:

*The spherical suspension over $S$ is homeomorphic to $\mathbb{S}^{m+1}$.*

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