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Izv. Akad. Nauk SSSR Ser. Mat., 1970, Volume 34, Issue 2, Pages 253–288 (Mi izv2415)  

This article is cited in 22 scientific papers (total in 22 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. I

S. P. Novikov


Abstract: The complicated and intricate algebraic material in smooth topology (the theory of surgery) does not fit into the already existing concepts of stable algebra. It turns out that the systematization of this material is most naturally carried through from the point of view of an algebraic version of the hamiltonian formalism over rings with involution. The present article is devoted to this task. The first part contains a development of the algebraic concepts.

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English version:
Mathematics of the USSR-Izvestiya, 1970, 4:2, 257–292

Bibliographic databases:

UDC: 513.8
MSC: 19G38, 57R20, 16W10, 55N20, 18F25
Received: 25.11.1969

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. I”, Izv. Akad. Nauk SSSR Ser. Mat., 34:2 (1970), 253–288; Math. USSR-Izv., 4:2 (1970), 257–292

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.~I
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1970
\vol 34
\issue 2
\pages 253--288
\mathnet{http://mi.mathnet.ru/izv2415}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=292913}
\zmath{https://zbmath.org/?q=an:0193.51902|0216.45003}
\transl
\jour Math. USSR-Izv.
\yr 1970
\vol 4
\issue 2
\pages 257--292
\crossref{https://doi.org/10.1070/IM1970v004n02ABEH000903}


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    This publication is cited in the following articles:
    1. 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”, Math. USSR-Izv., 4:3 (1970), 479–505  mathnet  crossref  mathscinet  zmath
    2. 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
    3. A. S. Mishchenko, “Infinite-dimensional representations of discrete groups, and higher signatures”, Math. USSR-Izv., 8:1 (1974), 85–111  mathnet  crossref  mathscinet  zmath
    4. V. P. Maslov, M. V. Fedoryuk, “The canonic operator (real case)”, J Math Sci, 3:2 (1975), 217  crossref  zmath
    5. 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
    6. 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
    7. L. N. Vaserstein, “Foundations of algebraic $K$-theory”, Russian Math. Surveys, 31:4 (1976), 89–156  mathnet  crossref  mathscinet  zmath
    8. V. A. Vardanyan, “On periodicity in Hermitian theories”, Russian Math. Surveys, 33:2 (1978), 253–254  mathnet  crossref  mathscinet  zmath
    9. 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
    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. Yu. V. Muranov, I. Hambleton, “Projective splitting obstruction groups for one-sided submanifolds”, Sb. Math., 190:10 (1999), 1465–1485  mathnet  crossref  crossref  mathscinet  zmath  isi
    14. Cavicchioli A. Muranov Y. Repovs D., “Algebraic Properties of Decorated Splitting Obstruction Groups”, Boll. Unione Mat. Italiana, 4B:3 (2001), 647–675  isi
    15. A. Ranicki, “Blanchfield and Seifert algebra in high-dimensional knot theory”, Mosc. Math. J., 3:4 (2003), 1333–1367  mathnet  crossref  mathscinet  zmath
    16. Nigel Higson, John Roe, “Mapping Surgery to Analysis I: Analytic Signatures”, K-Theory, 33:4 (2004), 277  crossref  mathscinet  zmath  isi
    17. Cavicchioli A. Muranov Y. Spaggiari F., “Relative Groups in Surgery Theory”, Bull. Belg. Math. Soc.-Simon Steven, 12:1 (2005), 109–135  isi
    18. St. Petersburg Math. J., 19:1 (2008), 159–165  mathnet  crossref  mathscinet  zmath  isi  elib
    19. 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
    20. EDGAR G. GOODAIRE, CÉSAR POLCINO MILIES, “ORIENTED INVOLUTIONS AND SKEW-SYMMETRIC ELEMENTS IN GROUP RINGS”, J. Algebra Appl, 12:01 (2013), 1250131  crossref
    21. 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
    22. 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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