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Classification of the congruence classes of A_n^5(n≥6) with 2-torsion free homology

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Science China Mathematics 2020年第7期63卷 1409-1428页

作者： Zhongjian Zhu Jianzhong Pan College of Mathematics Physics and Electronic Information EngineeringWenzhou UniversityWenzhou 325035China Hua Loo-Keng Key Laboratory of Mathematics Institute of MathematicsAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China

In this paper,we classify the congruence classes of Fn(2)5-polyhedra,i.e.,(n-1)-connected,at most(n+5)-dimensional polyhedra with 2-torsion free *** proof relies on the matrix problem technique which was developed in ... 详细信息

关键词： homotopy indecomposable matrix problem congruence class

Stable homotopy classification of A_n^4-polyhedra with 2-torsion free homology

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Science China Mathematics 2016年第6期59卷 1141-1162页

作者： PAN JianZhong ZHU ZhongJian HUA Loo-Keng Key Laboratory of Mathematics Academy of Mathematics and Systems ScienceChinese Academy of Sciences Academy of Mathematics and Systems Science Chinese Academy of Sciences

We study the stable homotopy types of F_n^4(2)-polyhedra, i.e.,(n- 1)-connected, at most(n+ 4)-dimensional polyhedra with 2-torsion free homologies. We are able to classify the indecomposable F_n^4(2)-polyhedra. The proof relies on the matrix problem technique which was developed in the classification of representations of algebras and applied to homotopy theory by Baues and Drozd(1999, 2001, 2004).

关键词： homotopy indecomposable matrix problem

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Unified tame theorem

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Science China Mathematics 2009年第9期52卷 2036-2068页

作者： ZHANG YingBo XU YunGe School of Mathematical Sciences Beijing Normal UniversityBeijing 100875China School of Mathematics and Computer Science Hubei UniversityWuhan 430062China

The well-known tame theorem tells that for a given tame bocs and a positive integer n there exist finitely many minimal bocses, such that any representation of the original bocs of dimension at most n is isomorphic to the image of a representation of some minimal bocses under a certain reduction functor. In the present paper we will give an alternative statement of the tame theorem in terms of matrix problem, by constructing a unified minimal matrix problem whose indecomposable matrices cover all the canonical forms of the indecomposable representations of dimension at most n for each non-negative integer n.

关键词： matrix problem canonical form representation tame type indecomposable 15A21 16G20 16G60 16G70