Future complete Einsteinian space times with U(1) symmetry, the unpolarized case

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I prove the existence of vacuum $S^{1}$ symmetric Einsteinian, unpolarized, space times which are complete in the direction of the expansion, for small initial data, without supposing that the $S^{1}$ orbits are orthogonal to the 3-manifolds, as was done in previous work in collaboration with V. Moncrief.
67 pages, text for the volume of the Cargese meeting "50 years of the Cauchy problem in General Relativity"

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