We heard and learned from that https://mathoverflow.net/questions/264330/not-all-manifolds-can-be-triangulated-in-which-dimensions. "All orientable 5-dimensional manifolds are triangulable. In dimensions at least 6, though, you can use their construction to produce non-triangulable orientable manifolds."


What are some examples of non-triangulable manifolds which are orientable and non-orientable?

>- Oreintable of non-triangulable manifolds, criteria and examples?

> - Non-Oreintable of non-triangulable manifolds, criteria and examples?


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>- 4-dimensional E$_8$-manifold is non-triangulable. But it is a spin manifold. Is E$_8$-manifold triangulable or not? Why and how to prove this?