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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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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
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\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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This publication is cited in the following articles:
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G. G. Kasparov, “Topological invariants of elliptic operators. I. $K$-homology”, Math. USSR-Izv., 9:4 (1975), 751–792
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A. S. Mishchenko, “On Fredholm representations of discrete groups”, Funct. Anal. Appl., 9:2 (1975), 121–125
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Yu. P. Solovev, “Diskretnye podgruppy, kompleksy Bryua–Titsa i gomotopicheskaya invariantnost vysshikh signatur”, UMN, 31:1(187) (1976), 261–262
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A. S. Mishchenko, “Hermitian $K$-theory. The theory of characteristic classes and methods of functional analysis”, Russian Math. Surveys, 31:2 (1976), 71–138
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A. S. Mishchenko, “Banach algebras, pseudodifferential operators, and their application to $K$-theory”, Russian Math. Surveys, 34:6 (1979), 77–91
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A. S. Mishchenko, Yu. P. Solov'ev, “Representations of Banach algebras and formulas of Hirzebruch type”, Math. USSR-Sb., 39:2 (1981), 189–205
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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
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Alain Connes, “Non-commutative differential geometry”, Publications Mathématiques de l’Institut des Hautes Études Scientifiques, 62:1 (1985), 41
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A. Connes, “Compact metric spaces, Fredholm modules, and hyperfiniteness”, Ergod Th Dynam Sys, 9:2 (1989)
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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
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Nigel Higson, John Roe, “Mapping Surgery to Analysis I: Analytic Signatures”, K-Theory, 33:4 (2004), 277
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Fabio Cipriani, Jean-Luc Sauvageot, “Fredholm Modules on P.C.F. Self-Similar Fractals and Their Conformal Geometry”, Comm Math Phys, 2008
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Savin A.Yu., Sternin B.Yu., “Uniformizatsiya nelokalnykh ellipticheskikh operatorov i \it{kk}-teoriya”, Doklady akademii nauk, 448:1 (2013), 27–27
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A. Yu. Savin, B. Yu. Sternin, “Uniformization of nonlocal elliptic operators and KK-theory”, Russ. J. Math. Phys, 20:3 (2013), 345
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Fabio Cipriani, Daniele Guido, Tommaso Isola, Jean-Luc Sauvageot, “Spectral triples for the Sierpinski gasket”, Journal of Functional Analysis, 2014
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G. Yu, “The Novikov conjecture”, Russian Math. Surveys, 74:3 (2019), 525–541
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