When a subset of locally lies on a sphere
The question in the title, first raised by Goldman and Donaldson, was partially answered by Reznikov. We give a complete answer, as follows: if can be realized as both the fundamental group of a closed 3-manifold and of a compact Kähler manifold, then must be finite—and thus belongs to the well-known list of finite subgroups of , acting freely on .
Given adjacent subanalytic strata in verifying Kuo’s ratio test (resp. Verdier’s -regularity) we find an open dense subset of the codimension submanifolds (wings) containing such that is generically Whitney -regular is exactly one more than the dimension...