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For questions requesting examples of a certain structure or phenomenon
21
votes
Failure of smoothing theory for topological 4-manifolds
Donaldson's and Freedman's results imply lots of examples of non-smoothable 4-manifolds with trivial Kirby-Siebenmann invariant: any unimodular intersection form arises from a closed simply connected topological …
13
votes
Accepted
Natural examples of finite dimensional spaces with interesting 2-type
The 2-type of a 4-manifold is an extremely interesting invariant. In fact, work of Hambleton and Kreck shows that in many cases it determines the homotopy type (if one adds the intersection form as an …