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Topology of real cubic fourfolds

Finashin, Sergey
Kharlamov, V.
A solution of the problem of topological classification of real cubic fourfolds is given. It is proven that the real locus of a real non-singular cubic fourfold is diffeomorphic either to a connected sum RP(4)#i(S(2) x S(2))# j(S(1) x S(3)) or to a disjoint union RP(4) (sic) S(4).