Matrix problems, triangulated categories and stable homotopy types

TL;DR

This paper explores the use of matrix problems in classifying stable homotopy types of polyhedra, providing new insights into their representation types and structure in finite and tame cases.

Contribution

It introduces a novel application of bimodule categories to triangulated categories and classifies stable homotopy types using matrix problem techniques.

Findings

Classification of stable homotopy types in finite and tame cases

Identification of representation types for these problems

Application of matrix problems to triangulated categories

Abstract

We show how matrix problems (bimodule categories) can be used in studying triangulated categories. Then we apply the general technique to the classification of stable homotopy types of polyhedra, find out the "representation types" of such problems and give a description of stable homotopy types in finite and tame cases.