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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).

13 votes

Independent evidence for the classification of topological 4-manifolds?

There is no other evidence. In fact there is absolutely no evidence what so ever. I have never met a mathematician who could convince me that he or she understood Freedman`s proof. I attempted to read …
Karl Luttinger's user avatar