Abstract:
A description of Fredholm representations as a particular case of graded representations is given. For graded representations of Banach algebras Hirzebruch type formulas are deduced by the method of bordism theory and the theory of bundles of algebraic Poincaré complexes.
Bibliography: 13 titles.
Citation:
A. S. Mishchenko, Yu. P. Solov'ev, “Representations of Banach algebras and formulas of Hirzebruch type”, Math. USSR-Sb., 39:2 (1981), 189–205
\Bibitem{MisSol80}
\by A.~S.~Mishchenko, Yu.~P.~Solov'ev
\paper Representations of Banach algebras and formulas of Hirzebruch type
\jour Math. USSR-Sb.
\yr 1981
\vol 39
\issue 2
\pages 189--205
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Linking options:
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https://doi.org/10.1070/SM1981v039n02ABEH001482
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This publication is cited in the following 12 articles:
V. V. Belokurov, A. A. Egorov, A. S. Mishchenko, F. Yu. Popelenskii, V. A. Sadovnichii, E. V. Troitskii, A. T. Fomenko, E. T. Shavgulidze, “Yurii Petrovich Solov'ev (obituary)”, Russian Math. Surveys, 59:5 (2004), 941–947
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
Mishchenko, AS, “Theory of almost algebraic Poincaré complexes and local combinatorial Hirzebruch formula”, Acta Applicandae Mathematicae, 68:1–3 (2001), 5
A. S. Mishchenko, “A Theory of Almost Algebraic Poincaré Complexes”, Proc. Steklov Inst. Math., 231 (2000), 281–307
A. S. Mishchenko, “Local Combinatorial Hirzebruch Formula”, Proc. Steklov Inst. Math., 224 (1999), 226–239
Hilsum M., Skandalis G., “Homotopy-Invariance of the Coefficient Signature in a Quasi-Flat Bundle (Connes-Gromov-Moscovici Method)”, J. Reine Angew. Math., 423 (1992), 73–99
Skandalis G., “Approach to the Novikov-Conjecture by a Cyclic Cohomology (According to Connes,a. Gromov,M. and Moscovici,H.)”, Asterisque, 1991, no. 201, 299–320
Troitsky E., “An Exact K-Cohomological C-Star-Index Formula .1. Thom Isomorphism and Topological Index”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 1988, no. 2, 83–85
Kasparov G., “Equivariant Kk-Theory and the Novikov-Conjecture”, Invent. Math., 91:1 (1988), 147–201
Papatriantafillou M., “Finsler Structures on a-Bundles”, Math. Nachr., 130 (1987), 75–85
V. M. Manuilov, “K-homology of C∗-algebras”, Math. USSR-Sb., 59:2 (1988), 533–540
E. V. Troitskii, “On the connection between complex and operator topological equivariant K-theories”, Russian Math. Surveys, 40:4 (1985), 243–244
Citation in format AMSBIB
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