The stable homotopy classification of $(n-1)$-connected $(n+4)$-dimensional polyhedra with 2 torsion free homology

TL;DR

This paper classifies the stable homotopy types of certain highly connected, low-dimensional polyhedra with torsion-free homology, using matrix problem techniques from algebraic representation theory.

Contribution

It provides a classification of indecomposable $(n-1)$-connected, $(n+4)$-dimensional polyhedra with 2-torsion free homology, extending homotopy classification methods.

Findings

Classified indecomposable $ extbf{F}^4_{n(2)}$-polyhedra.

Applied matrix problem techniques to homotopy classification.

Extended algebraic methods to topological classification.

Abstract

In this paper, we study the stable homotopy types of $\mathbf{F}^4_{n(2)}$-polyhedra, i.e., $(n-1)$-connected, at most $(n+4)$-dimensional polyhedra with 2-torsion free homologies. We are able to classify the indecomposable $\mathbf{F}^4_{n(2)}$-polyhedra. The proof relies on the matrix problem technique which was developed in the classification of representaions of algebras and applied to homotopy theory by Baues and Drozd.