Furuta theorem

Furuta’s theorem (also called 10/8 theorem) describes which indefinite even intersection forms arise from oriented closed smooth 4-manifolds. (According to Freedman's classification, all can from simply connected oriented closed topological 4-manifolds, which makes smoothness the crucial property.) It comes down to the forms: according to Serre’s classification theorem with Rokhlin's theorem requiring an even number of definite and indefiniteness requiring . Simon Donaldson furthermore showed,..