What’s hot at mathoverflow 18/17

Open subsets of Euclidean space in dimension 5 and higher admitting exotic smooth structures

Can a finite group action by homeomorphisms of a three-manifold be approximated by a smooth action?

Can a sphere glued into a soft 3d-mattress rotate continuously? (manifolds, SU(2) and the belt trick)

Does the image of the exponential map generate the group?

Examples of interesting non orientable closed 3-manifolds

Is there a closed 5-manifold M with \(w_1(M)w_2(M)\not=0\)?

Examples of triality in mathematics

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