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Let $M$ be a smooth manifold. Let $K$ be a simplicial complex. Let ${\rm sd}(K)$ be the sub-division of $K$. Suppose there exists a simplicial sub-complex $K_1$ of ${\rm sd}(K)$ such that $K_1$ ...

If $X_d$ is a non-triangulable manifold, can $X_d \times T^k$, $X_d \times I^k$, or $X_d \times \mathbb{R}^k$ always be a triangulable manifold? Let $X_d$ be a $d$-manifold which is NOT a ...

I was reading a review article arXiv:1310.7644 and it was explained there that in the last few years it was proven that there are topological manifolds of dimension greater than four that cannot be ...

We heard and learned from Mike Miller's answer to Not all manifolds can be triangulated: In which dimensions? that "All orientable 5-dimensional manifolds are triangulable. In dimensions at least ...