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

This article is cited in 21 scientific papers (total in 21 papers)

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
Received: 25.12.1969

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  mathnet  crossref  mathscinet  zmath
    2. A. S. Mishchenko, “Infinite-dimensional representations of discrete groups, and higher signatures”, Math. USSR-Izv., 8:1 (1974), 85–111  mathnet  crossref  mathscinet  zmath
    3. G. G. Kasparov, “Topological invariants of elliptic operators. I. $K$-homology”, Math. USSR-Izv., 9:4 (1975), 751–792  mathnet  crossref  mathscinet  zmath
    4. A. F. Kharshiladze, “Manifolds of the homotopy type of the product of two projective spaces”, Math. USSR-Sb., 25:4 (1975), 471–486  mathnet  crossref  mathscinet  zmath
    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  mathnet  crossref  mathscinet  zmath
    6. L. N. Vaserstein, “Foundations of algebraic $K$-theory”, Russian Math. Surveys, 31:4 (1976), 89–156  mathnet  crossref  mathscinet  zmath
    7. V. A. Vardanyan, “On periodicity in Hermitian theories”, Russian Math. Surveys, 33:2 (1978), 253–254  mathnet  crossref  mathscinet  zmath
    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  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    9. A. A. Bovdi, “Unitarity of the multiplicative group of an integral group ring”, Math. USSR-Sb., 47:2 (1984), 377–389  mathnet  crossref  mathscinet  zmath
    10. V. G. Turaev, “A cocycle for the symplectic first chern class and the maslov index”, Funct. Anal. Appl., 18:1 (1984), 35–39  mathnet  crossref  mathscinet  zmath  isi
    11. A. F. Kharshiladze, “Surgery on manifolds with finite fundamental groups”, Russian Math. Surveys, 42:4 (1987), 65–103  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    12. S. P. Novikov, “The Schrödinger operator on graphs and topology”, Russian Math. Surveys, 52:6 (1997), 1320–1321  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    13. Cavicchioli A. Muranov Y. Repovs D., “Algebraic Properties of Decorated Splitting Obstruction Groups”, Boll. Unione Mat. Italiana, 4B:3 (2001), 647–675  isi
    14. A. Ranicki, “Blanchfield and Seifert algebra in high-dimensional knot theory”, Mosc. Math. J., 3:4 (2003), 1333–1367  mathnet  crossref  mathscinet  zmath
    15. Nigel Higson, John Roe, “Mapping Surgery to Analysis I: Analytic Signatures”, K-Theory, 33:4 (2004), 277  crossref  mathscinet  zmath  isi
    16. Cavicchioli A. Muranov Y. Spaggiari F., “Relative Groups in Surgery Theory”, Bull. Belg. Math. Soc.-Simon Steven, 12:1 (2005), 109–135  isi
    17. St. Petersburg Math. J., 19:1 (2008), 159–165  mathnet  crossref  mathscinet  zmath  isi  elib
    18. A. Bak, Yu. V. Muranov, “Splitting a simple homotopy equivalence along a submanifold with filtration”, Sb. Math., 199:6 (2008), 787–809  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    20. E.G.. GOODAIRE, CÉS.P.OLCINO MILIES, “ORIENTED INVOLUTIONS AND SKEW-SYMMETRIC ELEMENTS IN GROUP RINGS”, J. Algebra Appl, 12:01 (2013), 1250131  crossref
    21. G. Yu, “The Novikov conjecture”, Russian Math. Surveys, 74:3 (2019), 525–541  mathnet  crossref  crossref  adsnasa  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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