Geodesic
Homotopy invariants of nonsimply connected manifolds. III. Higher signatures
Izvestiya. Mathematics, Tome 5 (1971) no. 6, pp. 1325-1364 
A. S. Mishchenko. Homotopy invariants of nonsimply connected manifolds. III. Higher signatures. Izvestiya. Mathematics, Tome 5 (1971) no. 6, pp. 1325-1364. http://geodesic.mathdoc.fr/item/IM2_1971_5_6_a7/
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     title = {Homotopy invariants of nonsimply connected {manifolds.~III.} {Higher} signatures},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The homotopy invariance of the higher signatures of nonsimply connected manifolds is proved in this paper. The method of proof is based on the study of absolute invariants of nonsimply connected manifolds similar to algebraic $K$-theory and on the construction of an analog to intersection theory for Poincaré complexes.

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