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Matrix problems and stable homotopy types of polyhedra. (English) Zbl 1062.55004

Summary: 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 [Expo. Math. 17, 161–179 (1999; Zbl 0542.55010); Topology 40, 789–821 (2001; Zbl 0984.55006); Contemp. Math. 274, 39–56 (2001; Zbl 0979.55006)]. The proofs are based on the technique of matrix problems (bimodule categories).

MSC:

55P15 Classification of homotopy type
15B36 Matrices of integers
16G60 Representation type (finite, tame, wild, etc.) of associative algebras
55P10 Homotopy equivalences in algebraic topology
55P42 Stable homotopy theory, spectra
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References:

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