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If a polyhedron in $\mathbb{R}^3$ has local intersections, does it also have more global intersections?
Consider a simplicial complex $K$. A piecewise linear map $f: K \to \mathbb{R}^n$ is an almost-embedding if $f(\sigma) \cap f(\tau) = \emptyset$ for any two disjoint simplices $\sigma,\tau$ in $K$.
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Is every simplicial $d$-sphere linearly embeddable in $\Bbb R^{d+1}$?
A simplicial $d$-sphere is a simplicial complex homeomorphic to the $d$-sphere. It is known that not every such complex can be embedded into $\Bbb R^{d+1}$ as the boundary complex of a convex ...
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