Packet 5: Tossup 20

John Milnor constructed an “exotic” differentiable manifold that is (15[1])homeomorphic (15[1])but not diffeomorphic to these objects in dimension seven. (15[3])Stereographic projection is used to map points (15[1])on one of these objects (-5[1])to the complex (15[1])plane. (15[2])The idea that (15[1]-5[1])every (15[1])simply connected (15[1])closed 3-manifold is homeomorphic (15[1])to one of these (15[1])surfaces (15[1])was (15[1])the subject (15[1])of the (*) Poincaré (10[1])(“pwann-cah-RAY”) conjecture (10[1])that (10[1])Grigory Perelman proved. A coordinate system named for these objects utilizes (10[1])polar and azimuthal angles. (10[1]-5[2])For 10 points, name (10[1])these objects, (10[1]-5[1])which contain all points equidistant (10[1])from a center (10[1]-5[1])in (-5[1])three (10[1]-5[2])dimensions. ■END■ (10[11])

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