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Izv. Akad. Nauk SSSR Ser. Mat., 1971, Volume 35, Issue 6, Pages 1316–1355 (Mi izv2173)  

This article is cited in 5 scientific papers (total in 6 papers)

Homotopy invariants of nonsimply connected manifolds. III. Higher signatures

A. S. Mishchenko


Abstract: 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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English version:
Mathematics of the USSR-Izvestiya, 1971, 5:6, 1325–1364

Bibliographic databases:

UDC: 513.8
MSC: Primary 57D65, 57B10; Secondary 57C10, 57C20, 57D10
Received: 07.05.1971

Citation: A. S. Mishchenko, “Homotopy invariants of nonsimply connected manifolds. III. Higher signatures”, Izv. Akad. Nauk SSSR Ser. Mat., 35:6 (1971), 1316–1355; Math. USSR-Izv., 5:6 (1971), 1325–1364

Citation in format AMSBIB
\Bibitem{Mis71}
\by A.~S.~Mishchenko
\paper Homotopy invariants of nonsimply connected manifolds.~III. Higher signatures
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1971
\vol 35
\issue 6
\pages 1316--1355
\mathnet{http://mi.mathnet.ru/izv2173}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=293658}
\zmath{https://zbmath.org/?q=an:0248.57014}
\transl
\jour Math. USSR-Izv.
\yr 1971
\vol 5
\issue 6
\pages 1325--1364
\crossref{https://doi.org/10.1070/IM1971v005n06ABEH001248}


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    This publication is cited in the following articles:
    1. S. B. Shlosman, “Smooth structures on Poincaré complexes”, Math. USSR-Izv., 7:4 (1973), 919–932  mathnet  crossref  mathscinet  zmath
    2. A. S. Mishchenko, “Infinite-dimensional representations of discrete groups, and higher signatures”, Math. USSR-Izv., 8:1 (1974), 85–111  mathnet  crossref  mathscinet  zmath
    3. A. S. Mishchenko, “Hermitian $K$-theory. The theory of characteristic classes and methods of functional analysis”, Russian Math. Surveys, 31:2 (1976), 71–138  mathnet  crossref  mathscinet  zmath
    4. Yu. P. Solov'ev, “Signature realizable subgroups of the Wall group”, Russian Math. Surveys, 36:3 (1981), 266–267  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. S. V. Lapin, “Bordism groups of Poincare $E_\infty$-coalgebras and symmetric $L$-groups”, Sb. Math., 186:7 (1995), 1023–1055  mathnet  crossref  mathscinet  zmath  isi
    6. A. A. Bolibrukh, A. A. Irmatov, M. I. Zelikin, O. B. Lupanov, V. M. Maynulov, E. F. Mishchenko, M. M. Postnikov, Yu. P. Solov'ev, E. V. Troitskii, “Aleksandr Sergeevich Mishchenko (on his 60th birthday)”, Russian Math. Surveys, 56:6 (2001), 1187–1191  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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