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Topology of cell complexes and manifolds, classification of manifolds (e.g. smoothing, surgery), low dimensional topology (e.g. knot theory, invariants of 4-manifolds), embedding theory, combinatorial and PL topology, geometric group theory, infinite dimensional topology (e.g. Hilbert cube manifolds, theory of retracts).
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What is the 'non-intuitive' part in sphere eversion (turning inside out)?
The question does not mean sphere eversion is intuitive to me! In fact, it is just the opposite and that is the purpose of this question.
Recently, I was reading about Smale's paradox, the problem o …