Abstract:
A survey of basic technical constructions associated with the KK-bifunctor is given along with main results obtained through it, statements of unsolved problems are given, some hypotheses are stated.
Citation:
G. G. Kasparov, “Operator KK-theory and its applications”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh., 27, VINITI, Moscow, 1985, 3–31; J. Soviet Math., 37:6 (1987), 1373–1396
\Bibitem{Kas85}
\by G.~G.~Kasparov
\paper Operator $K$-theory and its applications
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh.
\yr 1985
\vol 27
\pages 3--31
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/intd84}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=824259}
\zmath{https://zbmath.org/?q=an:0616.46064}
\transl
\jour J. Soviet Math.
\yr 1987
\vol 37
\issue 6
\pages 1373--1396
\crossref{https://doi.org/10.1007/BF01103851}
Linking options:
https://www.mathnet.ru/eng/intd84
https://www.mathnet.ru/eng/intd/v27/p3
This publication is cited in the following 6 articles:
Fabian R. Lux, Tom Stoiber, Shaoyun Wang, Guoliang Huang, Emil Prodan, “Topological spectral bands with frieze groups”, Journal of Mathematical Physics, 65:6 (2024)
Emil Prodan, “Topological lattice defects by groupoid methods and Kasparov's KK-theory*”, J. Phys. A: Math. Theor., 54:42 (2021), 424001
Maria Paula Gomez Aparicio, Pierre Julg, Alain Valette, Advances in Noncommutative Geometry, 2019, 127
Emil Prodan, Hermann Schulz-Baldes, “Generalized Connes–Chern characters inKK-theory with an application to weak invariants of topological insulators”, Rev. Math. Phys., 28:10 (2016), 1650024
V. E. Nazaikinskii, A. Yu. Savin, B. Yu. Sternin, “On the Poincaré isomorphism in $K$-theory on manifolds with edges”, Journal of Mathematical Sciences, 170:2 (2010), 238–250
B. A. Plamenevskii, G. V. Rozenblum, “Pseudodifferential operators with discontinuous symbols: $K$-theory and the index formula”, Funct. Anal. Appl., 26:4 (1992), 266–275
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