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For questions requesting examples of a certain structure or phenomenon

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 …
Peter Teichner's user avatar
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 …
Peter Teichner's user avatar