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2004 | 2 | 3 | 420-447
Tytuł artykułu

Matrix problems and stable homotopy types of polyhedra

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Treść / Zawartość
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Języki publikacji
EN
Abstrakty
EN
This is a survey of the results on stable homotopy types of polyhedra of small dimensions, mainly obtained by H.-J. Baues and the author [3, 5, 6]. The proofs are based on the technique of matrix problems (bimodule categories).
Wydawca
Czasopismo
Rocznik
Tom
2
Numer
3
Strony
420-447
Opis fizyczny
Daty
wydano
2004-06-01
online
2004-06-01
Twórcy
autor
Bibliografia
  • [1] H.J. Baues:Homotopy Type and Homology, Oxford University Press, 1996.
  • [2] H.J. Baues: “Atoms of Topology”,Jahresber. Dtsch. Math.-Ver., Vol. 104, (2002), pp. 147–164.
  • [3] H.J. Baues add Yu. A. Drozd: “The homotopy classification of (n−1)-connected (n+4)-dimensional polyhedra with torsion free homology”,Expo. Math., Vol. 17, (1999), pp. 161–179.
  • [4] H.J. Baues and Yu. A. Drozd: “Representation theory of homotopy types with at most two non-trivial homotopy groups”,Math. Proc. Cambridge Phil. Soc., Vol. 128, (2000), pp. 283–300. http://dx.doi.org/10.1017/S0305004199004168
  • [5] H.J. Baues and Yu. A. Drozd: “Indecomposable homotopy types with at most two non-trivial homology groups, in: Groups of Homotopy Self-Equivalences and Related Topics”,Contemporary Mathematics, Vol. 274, (2001), pp. 39–56.
  • [6] H.J. Baues and Yu. A. Drozd: “Classification of stable homotopy types with torsion-free homology”. Topology,Vol 40, (2001),pp. 789–821. http://dx.doi.org/10.1016/S0040-9383(99)00084-1
  • [7] H.J. Baues and Hennes: “The homotopy classification of (n−1)-connected (n+3)-dimensional polyhedra,n≥4”,Topology, Vol. 30, (1991), pp. 373–408. http://dx.doi.org/10.1016/0040-9383(91)90020-5
  • [8] V.M. Bondarenko: “Representations of bundles of semichained sets and their applications”,St. Petersburg Math. J., Vol. 3, (1992), pp. 973–996.
  • [9] S.C. Chang: “Homotopy invariants and continuous mappings”,Proc. R. Soc. London, Vol. 202, (1950), pp. 253–263. http://dx.doi.org/10.1098/rspa.1950.0098
  • [10] J.M. Cohen:Stable Homotopy, Lecture Notes in Math., Springer-Verlag, 1970.
  • [11] Yu.A. Drozd: “Matrix problems and categories of matrices”,Zapiski Nauch. Semin. LOMI, Vol. 28, (1972), pp. 144–153.
  • [12] Yu.A. Drozd: “Finitely generated quadratic modules”, Manus. Math,Vol 104, (2001),pp. 239–256. http://dx.doi.org/10.1007/s002290170041
  • [13] Yu.A. Drozd: “Reduction algorithm and representations of boxes and algebras”,Comptes Rendues Math. Acad. Sci. Canada, Vol. 23, (2001), pp. 97–125.
  • [14] P. Freyd: “Stable homotopy II. Applications of Categorical Algebra”,Proc. Symp. Pure Math., Vol. 17, (1970), pp. 161–191.
  • [15] I.M. Gelfand and V.A. Ponomarev: “Remarks on the classification of a pair of commuting linear transformations in a finite-dimensional space”,Funk. Anal. Prilozh., Vol. 3:4, (1969), pp. 81–82.
  • [16] S.I. Gelfand and Yu.I. Manin:Methods of Homological Algebra, Springer-Verlag, 1996.
  • [17] H.W. Henn: “Classification ofp-local low dimensiona; spectra”,J. Pure and Appl. Algebra, Vol. 45, (1987), pp. 45–71. http://dx.doi.org/10.1016/0022-4049(87)90083-1
  • [18] Hu Sze-Tsen:Homotopy Theory, Academic Press, 1959.
  • [19] E. Spanier:Algebraic Topology, McGraw-Hill, 1966.
  • [20] R.M. Switzer:Algebraic Topology-Homotopy and Homology, Springer-Verlag, 1975.
  • [21] H. Toda:Composition Methods in the Homotopy Groups of Spheres, Ann. Math. Studies, Vol. 49, Princeton, 1962.
  • [22] H.M. Unsöld: “A n 4-Polyhedra with free homology”,Manus. Math., Vol. 65, (1989), pp. 123–145. http://dx.doi.org/10.1007/BF01168295
  • [23] J.H.C. Whitehead: “The homotopy type of a special kind of polyhedron”,Ann. Soc. Polon. Math., Vol. 21, (1948), pp. 176–186.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_BF02475238
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