Matrix problems and stable homotopy types of polyhedra

Yuriy Drozd

Open Mathematics (2004)

  • Volume: 2, Issue: 3, page 420-447
  • ISSN: 2391-5455

Abstract

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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).

How to cite

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Yuriy Drozd. "Matrix problems and stable homotopy types of polyhedra." Open Mathematics 2.3 (2004): 420-447. <http://eudml.org/doc/268847>.

@article{YuriyDrozd2004,
abstract = {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).},
author = {Yuriy Drozd},
journal = {Open Mathematics},
keywords = {55P12; 15A36; 16G60},
language = {eng},
number = {3},
pages = {420-447},
title = {Matrix problems and stable homotopy types of polyhedra},
url = {http://eudml.org/doc/268847},
volume = {2},
year = {2004},
}

TY - JOUR
AU - Yuriy Drozd
TI - Matrix problems and stable homotopy types of polyhedra
JO - Open Mathematics
PY - 2004
VL - 2
IS - 3
SP - 420
EP - 447
AB - 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).
LA - eng
KW - 55P12; 15A36; 16G60
UR - http://eudml.org/doc/268847
ER -

References

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  1. [1] H.J. Baues:Homotopy Type and Homology, Oxford University Press, 1996. 
  2. [2] H.J. Baues: “Atoms of Topology”,Jahresber. Dtsch. Math.-Ver., Vol. 104, (2002), pp. 147–164. Zbl1013.55001
  3. [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. Zbl0942.55010
  4. [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 Zbl0959.55006
  5. [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. Zbl0979.55006
  6. [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 Zbl0984.55006
  7. [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 
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