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 Izv. Akad. Nauk SSSR Ser. Mat., 1970, Volume 34, Issue 3, Pages 475–500 (Mi izv2430)

Algebraic construction and properties of Hermitian analogs of $K$-theory over rings with involution from the viewpoint of Hamiltonian formalism. applications to differential topology and the theory of characteristic classes. II

S. P. Novikov

Abstract: The present paper is an immediate continuation of the author's paper [22]. Except in the last section, it is implicitly assumed here, as in [22], that the underlying ring contains 1/2 and all the theorems relate to the theory $U\otimes Z[1/2]$ without further comment.

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English version:
Mathematics of the USSR-Izvestiya, 1970, 4:3, 479–505

Bibliographic databases:

UDC: 513.8
MSC: 19G38, 57R20

Citation: S. P. Novikov, “Algebraic construction and properties of Hermitian analogs of $K$-theory over rings with involution from the viewpoint of Hamiltonian formalism. applications to differential topology and the theory of characteristic classes. II”, Izv. Akad. Nauk SSSR Ser. Mat., 34:3 (1970), 475–500; Math. USSR-Izv., 4:3 (1970), 479–505

Citation in format AMSBIB
\Bibitem{Nov70} \by S.~P.~Novikov \paper Algebraic construction and properties of Hermitian analogs of $K$-theory over rings with involution from the viewpoint of Hamiltonian formalism. applications to differential topology and the theory of characteristic classes.~II \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1970 \vol 34 \issue 3 \pages 475--500 \mathnet{http://mi.mathnet.ru/izv2430} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=292913} \zmath{https://zbmath.org/?q=an:0201.25602} \transl \jour Math. USSR-Izv. \yr 1970 \vol 4 \issue 3 \pages 479--505 \crossref{https://doi.org/10.1070/IM1970v004n03ABEH000916} 

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This publication is cited in the following articles:
1. I. A. Volodin, “Algebraic $K$-theory as extraordinary homology theory on the category of associative rings with unity”, Math. USSR-Izv., 5:4 (1971), 859–887
2. A. S. Mishchenko, “Infinite-dimensional representations of discrete groups, and higher signatures”, Math. USSR-Izv., 8:1 (1974), 85–111
3. G. G. Kasparov, “Topological invariants of elliptic operators. I. $K$-homology”, Math. USSR-Izv., 9:4 (1975), 751–792
4. A. F. Kharshiladze, “Manifolds of the homotopy type of the product of two projective spaces”, Math. USSR-Sb., 25:4 (1975), 471–486
5. A. S. Mishchenko, “Hermitian $K$-theory. The theory of characteristic classes and methods of functional analysis”, Russian Math. Surveys, 31:2 (1976), 71–138
6. L. N. Vaserstein, “Foundations of algebraic $K$-theory”, Russian Math. Surveys, 31:4 (1976), 89–156
7. V. A. Vardanyan, “On periodicity in Hermitian theories”, Russian Math. Surveys, 33:2 (1978), 253–254
8. V. E. Nazaikinskii, V. G. Oshmyan, B. Yu. Sternin, V. E. Shatalov, “Fourier integral operators and the canonical operator”, Russian Math. Surveys, 36:2 (1981), 93–161
9. A. A. Bovdi, “Unitarity of the multiplicative group of an integral group ring”, Math. USSR-Sb., 47:2 (1984), 377–389
10. V. G. Turaev, “A cocycle for the symplectic first chern class and the maslov index”, Funct. Anal. Appl., 18:1 (1984), 35–39
11. A. F. Kharshiladze, “Surgery on manifolds with finite fundamental groups”, Russian Math. Surveys, 42:4 (1987), 65–103
12. S. P. Novikov, “The Schrödinger operator on graphs and topology”, Russian Math. Surveys, 52:6 (1997), 1320–1321
13. Cavicchioli A. Muranov Y. Repovs D., “Algebraic Properties of Decorated Splitting Obstruction Groups”, Boll. Unione Mat. Italiana, 4B:3 (2001), 647–675
14. A. Ranicki, “Blanchfield and Seifert algebra in high-dimensional knot theory”, Mosc. Math. J., 3:4 (2003), 1333–1367
15. Nigel Higson, John Roe, “Mapping Surgery to Analysis I: Analytic Signatures”, K-Theory, 33:4 (2004), 277
16. Cavicchioli A. Muranov Y. Spaggiari F., “Relative Groups in Surgery Theory”, Bull. Belg. Math. Soc.-Simon Steven, 12:1 (2005), 109–135
17. St. Petersburg Math. J., 19:1 (2008), 159–165
18. A. Bak, Yu. V. Muranov, “Splitting a simple homotopy equivalence along a submanifold with filtration”, Sb. Math., 199:6 (2008), 787–809
19. P. G. Grinevich, S. P. Novikov, “Discrete $SL_n$-connections and self-adjoint difference operators on two-dimensional manifolds”, Russian Math. Surveys, 68:5 (2013), 861–887
20. E.G.. GOODAIRE, CÉS.P.OLCINO MILIES, “ORIENTED INVOLUTIONS AND SKEW-SYMMETRIC ELEMENTS IN GROUP RINGS”, J. Algebra Appl, 12:01 (2013), 1250131
21. G. Yu, “The Novikov conjecture”, Russian Math. Surveys, 74:3 (2019), 525–541
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