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Izv. Akad. Nauk SSSR Ser. Mat., 1974, Volume 38, Issue 1, Pages 81–106 (Mi izv1893)  

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

Infinite-dimensional representations of discrete groups, and higher signatures

A. S. Mishchenko


Abstract: In this article, we investigate a special class of representations of discrete groups. Making use of a number of geometrical constructions, we establish various relations between the Wall group of the fundamental group of a manifold, the higher signatures, and the $K$-theory of the classifying space of the fundamental group.

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English version:
Mathematics of the USSR-Izvestiya, 1974, 8:1, 85–111

Bibliographic databases:

UDC: 513.8
MSC: Primary 58B15; Secondary 20C99, 55B15, 57E25
Received: 08.12.1972

Citation: A. S. Mishchenko, “Infinite-dimensional representations of discrete groups, and higher signatures”, Izv. Akad. Nauk SSSR Ser. Mat., 38:1 (1974), 81–106; Math. USSR-Izv., 8:1 (1974), 85–111

Citation in format AMSBIB
\Bibitem{Mis74}
\by A.~S.~Mishchenko
\paper Infinite-dimensional representations of discrete groups, and higher signatures
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1974
\vol 38
\issue 1
\pages 81--106
\mathnet{http://mi.mathnet.ru/izv1893}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=0362407}
\zmath{https://zbmath.org/?q=an:0292.57017}
\transl
\jour Math. USSR-Izv.
\yr 1974
\vol 8
\issue 1
\pages 85--111
\crossref{https://doi.org/10.1070/IM1974v008n01ABEH002097}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. G. G. Kasparov, “Topological invariants of elliptic operators. I. $K$-homology”, Math. USSR-Izv., 9:4 (1975), 751–792  mathnet  crossref  mathscinet  zmath
    2. A. S. Mishchenko, “On Fredholm representations of discrete groups”, Funct. Anal. Appl., 9:2 (1975), 121–125  mathnet  crossref  mathscinet  zmath
    3. Yu. P. Solovev, “Diskretnye podgruppy, kompleksy Bryua–Titsa i gomotopicheskaya invariantnost vysshikh signatur”, UMN, 31:1(187) (1976), 261–262  mathnet  mathscinet  zmath
    4. 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
    5. A. S. Mishchenko, “Banach algebras, pseudodifferential operators, and their application to $K$-theory”, Russian Math. Surveys, 34:6 (1979), 77–91  mathnet  crossref  mathscinet  zmath
    6. 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
    7. Pierre Julg, Alain Valette, “K-theoretic amenability for SL2(Qp), and the action on the associated tree”, Journal of Functional Analysis, 58:2 (1984), 194  crossref
    8. Alain Connes, “Non-commutative differential geometry”, Publications Mathématiques de l’Institut des Hautes Études Scientifiques, 62:1 (1985), 41  crossref  zmath
    9. A. Connes, “Compact metric spaces, Fredholm modules, and hyperfiniteness”, Ergod Th Dynam Sys, 9:2 (1989)  crossref  mathscinet  zmath
    10. 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
    11. Nigel Higson, John Roe, “Mapping Surgery to Analysis I: Analytic Signatures”, K-Theory, 33:4 (2004), 277  crossref  mathscinet  zmath  isi
    12. Fabio Cipriani, Jean-Luc Sauvageot, “Fredholm Modules on P.C.F. Self-Similar Fractals and Their Conformal Geometry”, Comm Math Phys, 2008  crossref  mathscinet  isi
    13. Savin A.Yu., Sternin B.Yu., “Uniformizatsiya nelokalnykh ellipticheskikh operatorov i \it{kk}-teoriya”, Doklady akademii nauk, 448:1 (2013), 27–27  elib
    14. A. Yu. Savin, B. Yu. Sternin, “Uniformization of nonlocal elliptic operators and KK-theory”, Russ. J. Math. Phys, 20:3 (2013), 345  crossref
    15. Fabio Cipriani, Daniele Guido, Tommaso Isola, Jean-Luc Sauvageot, “Spectral triples for the Sierpinski gasket”, Journal of Functional Analysis, 2014  crossref
    16. G. Yu, “Gipoteza Novikova”, UMN, 74:3(447) (2019), 167–184  mathnet  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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