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Matrix problems and stable homotopy types of polyhedra

100%
Drozd Y.
Open Mathematics
|
2004
|
tom 2
|
nr 3
420-447
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).
2
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On genera of polyhedra

64%
Drozd Y., Kolesnyk P.
Open Mathematics
|
2012
|
tom 10
|
nr 2
401-410
EN
We consider the stable homotopy category S of polyhedra (finite cell complexes). We say that two polyhedra X,Y are in the same genus and write X ∼ Y if X p ≅ Y p for all prime p, where X p denotes the image of Xin the localized category S p. We prove that it is equivalent to the stable isomorphism X∨B 0 ≅Y∨B 0, where B 0 is the wedge of all spheres S n such that π nS(X) is infinite. We also prove that a stable isomorphism X ∨ X ≅ Y ∨ X implies a stable isomorphism X ≅ Y.
3
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Stable vector bundles over cuspidal cubics

64%
Bodnarchuk L., Drozd Y.
Open Mathematics
|
2003
|
tom 1
|
nr 4
650-660
EN
We give a complete classification of stable vector bundles over a cuspidal cubic and calculate their cohomologies. The technique of matrix problems is used, similar to [2, 3].
4
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On Cohen-Macaulay modules over non-commutative surface singularities

64%
Drozd Y., Gavran V.
Open Mathematics
|
2014
|
tom 12
|
nr 5
675-687
EN
We generalize the results of Kahn about a correspondence between Cohen-Macaulay modules and vector bundles to non-commutative surface singularities. As an application, we give examples of non-commutative surface singularities which are not Cohen-Macaulay finite, but are Cohen-Macaulay tame.
5
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On Hom-spaces of tame algebras

51%
Bautista R., Drozd Y., Zeng X., Zhang Y.
Open Mathematics
|
2007
|
tom 5
|
nr 2
215-263
EN
Let Λ be a finite dimensional algebra over an algebraically closed field k and Λ has tame representation type. In this paper, the structure of Hom-spaces of all pairs of indecomposable Λ-modules having dimension smaller than or equal to a fixed natural number is described, and their dimensions are calculated in terms of a finite number of finitely generated Λ-modules and generic Λ-modules. In particular, such spaces are essentially controlled by those of the corresponding generic modules.
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