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Izv. Akad. Nauk SSSR Ser. Mat., 1970, Volume 34, Issue 3, Pages 501–514 (Mi izv2431)  

This article is cited in 15 scientific papers (total in 16 papers)

Homotopy invariants of nonsimply connected manifolds. I. Rational invariants

A. S. Mishchenko


Abstract: Invariants of nonsimply connected manifolds are investigated of the same type as the signature of a manifold, or of “higher signature” for manifolds with free Abelian fundamental group, which correspond to the possibility of surgery on a manifold. It is proved that these invariants depend only on the homotopy type of the manifold and a bordism class of manifolds.

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English version:
Mathematics of the USSR-Izvestiya, 1970, 4:3, 506–519

Bibliographic databases:

UDC: 513.8
MSC: 57Txx, 58E05, 55N22, 57R60
Received: 15.12.1969

Citation: A. S. Mishchenko, “Homotopy invariants of nonsimply connected manifolds. I. Rational invariants”, Izv. Akad. Nauk SSSR Ser. Mat., 34:3 (1970), 501–514; Math. USSR-Izv., 4:3 (1970), 506–519

Citation in format AMSBIB
\Bibitem{Mis70}
\by A.~S.~Mishchenko
\paper Homotopy invariants of nonsimply connected manifolds. I.~Rational invariants
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1970
\vol 34
\issue 3
\pages 501--514
\mathnet{http://mi.mathnet.ru/izv2431}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=268898}
\zmath{https://zbmath.org/?q=an:0216.19701}
\transl
\jour Math. USSR-Izv.
\yr 1970
\vol 4
\issue 3
\pages 506--519
\crossref{https://doi.org/10.1070/IM1970v004n03ABEH000917}


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    This publication is cited in the following articles:
    1. A. S. Mischenko, “Gomotopicheskaya invariantnost vysshikh signatur neodnosvyaznykh mnogoobrazii”, UMN, 26:4(160) (1971), 239–240  mathnet  mathscinet  zmath
    2. A. S. Mishchenko, “Homotopy invariants of nonsimply connected manifolds. II: Simple homotopy type”, Math. USSR-Izv., 5:3 (1971), 668–679  mathnet  crossref  mathscinet  zmath
    3. A. S. Mishchenko, “Homotopy invariants of nonsimply connected manifolds. III. Higher signatures”, Math. USSR-Izv., 5:6 (1971), 1325–1364  mathnet  crossref  mathscinet  zmath
    4. A. S. Mischenko, “Beskonechnomernye predstavleniya diskretnykh grupp i gomotopicheskie invarianty neodnosvyaziykh mnogoobrazii”, UMN, 28:2(170) (1973), 239–240  mathnet  mathscinet  zmath
    5. A. S. Mishchenko, “Infinite-dimensional representations of discrete groups, and higher signatures”, Math. USSR-Izv., 8:1 (1974), 85–111  mathnet  crossref  mathscinet  zmath
    6. 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
    7. L. N. Vaserstein, “Foundations of algebraic $K$-theory”, Russian Math. Surveys, 31:4 (1976), 89–156  mathnet  crossref  mathscinet  zmath
    8. A. S. Mishchenko, A. T. Fomenko, “The index of elliptic operators over $C^*$-algebras”, Math. USSR-Izv., 15:1 (1980), 87–112  mathnet  crossref  mathscinet  zmath  isi
    9. A. S. Mishchenko, Yu. P. Solov'ev, “Representations of Banach algebras and formulas of Hirzebruch type”, Math. USSR-Sb., 39:2 (1981), 189–205  mathnet  crossref  mathscinet  zmath  isi
    10. V. M. Manuilov, “$K$-homology of $C^*$-algebras”, Math. USSR-Sb., 59:2 (1988), 533–540  mathnet  crossref  mathscinet  zmath
    11. 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
    12. A. S. Mishchenko, “Local Combinatorial Hirzebruch Formula”, Proc. Steklov Inst. Math., 224 (1999), 226–239  mathnet  mathscinet  zmath
    13. A. S. Mishchenko, “A Theory of Almost Algebraic Poincaré Complexes”, Proc. Steklov Inst. Math., 231 (2000), 281–307  mathnet  mathscinet  zmath
    14. 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
    15. Nigel Higson, John Roe, “Mapping Surgery to Analysis I: Analytic Signatures”, K-Theory, 33:4 (2004), 277  crossref  mathscinet  zmath  isi
    16. P. S. Popov, “Extension of the Hermitian $K$-theory functor and signature of topological manifolds”, Sb. Math., 198:8 (2007), 1145–1163  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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