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Izv. Akad. Nauk SSSR Ser. Mat., 1968, Volume 32, Issue 3, Pages 560–604 (Mi izv2478)  

This article is cited in 5 scientific papers (total in 8 papers)

$K$-theory on the category of infinite cell complexes

V. M. Buchstaber, A. S. Mishchenko


Abstract: The main purpose of the article is to compute cohomology operations in $K$-theory $\operatorname{mod}p$ and operations from the usual cohomology theory into $K$-theory. The proposed method is based on the extension of $K$-theory to a category of infinite complexes, which makes it possible to use spectral sequences of the “bar-construction” type.

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English version:
Mathematics of the USSR-Izvestiya, 1968, 2:3, 515–556

Bibliographic databases:

UDC: 513.83
MSC: 18F25, 18A20, 18G40, 18G15, 18G60, 19D55
Received: 15.05.1967

Citation: V. M. Buchstaber, A. S. Mishchenko, “$K$-theory on the category of infinite cell complexes”, Izv. Akad. Nauk SSSR Ser. Mat., 32:3 (1968), 560–604; Math. USSR-Izv., 2:3 (1968), 515–556

Citation in format AMSBIB
\Bibitem{BucMis68}
\by V.~M.~Buchstaber, A.~S.~Mishchenko
\paper $K$-theory on the category of infinite cell complexes
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1968
\vol 32
\issue 3
\pages 560--604
\mathnet{http://mi.mathnet.ru/izv2478}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=253322}
\zmath{https://zbmath.org/?q=an:0182.25803|0157.54001}
\transl
\jour Math. USSR-Izv.
\yr 1968
\vol 2
\issue 3
\pages 515--556
\crossref{https://doi.org/10.1070/IM1968v002n03ABEH000643}


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    Remarks

    This publication is cited in the following articles:
    1. L. N. Vaserstein, “Foundations of algebraic $K$-theory”, Russian Math. Surveys, 31:4 (1976), 89–156  mathnet  crossref  mathscinet  zmath
    2. A. N. Dranishnikov, “On a problem of P. S. Aleksandrov”, Math. USSR-Sb., 63:2 (1989), 539–545  mathnet  crossref  mathscinet  zmath
    3. A. N. Dranishnikov, “Homological dimension theory”, Russian Math. Surveys, 43:4 (1988), 11–63  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. Yu. B. Rudyak, “Orientability of bundles: obstruction theory and applications to $K$-theory”, Math. USSR-Sb., 68:2 (1991), 429–451  mathnet  crossref  mathscinet  zmath  isi
    5. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    6. A. A. Bolibrukh, A. P. Veselov, A. B. Zhizhchenko, I. M. Krichever, A. A. Mal'tsev, S. P. Novikov, T. E. Panov, Yu. M. Smirnov, “Viktor Matveevich Buchstaber (on his 60th birthday)”, Russian Math. Surveys, 58:3 (2003), 627–635  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    7. Manfred Stelzer, “Hyperbolic spaces at large primes and a conjecture of Moore”, Topology, 43:3 (2004), 667  crossref
    8. A. M. Vershik, A. P. Veselov, A. A. Gaifullin, B. A. Dubrovin, A. B. Zhizhchenko, I. M. Krichever, A. A. Mal'tsev, D. V. Millionshchikov, S. P. Novikov, T. E. Panov, A. G. Sergeev, I. A. Taimanov, “Viktor Matveevich Buchstaber (on his 70th birthday)”, Russian Math. Surveys, 68:3 (2013), 581–590  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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