Geodesic
Homotopy invariants of nonsimply connected manifolds.~III. Higher signatures
Izvestiya. Mathematics , Tome 5 (1971) no. 6, pp. 1325-1364

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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. 
@article{IM2_1971_5_6_a7,
     author = {A. S. Mishchenko},
     title = {Homotopy invariants of nonsimply connected {manifolds.~III.} {Higher} signatures},
     journal = {Izvestiya. Mathematics },
     pages = {1325--1364},
     publisher = {mathdoc},
     volume = {5},
     number = {6},
     year = {1971},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1971_5_6_a7/}
}
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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/