Self-Homotopy Equivalence Group of an Elliptic Space and Its Embedding in general Linear Groups

TL;DR

This paper explores the structure of the self-homotopy equivalence group of rational elliptic spaces and how it embeds into general linear groups, revealing new algebraic relationships.

Contribution

It provides a detailed analysis of the embedding of the self-homotopy equivalence group into linear groups for rational elliptic spaces, a novel connection in algebraic topology.

Findings

Identifies the embedding of the self-homotopy group into general linear groups.

Establishes algebraic relationships between homotopy groups and self-equivalence groups.

Provides new insights into the structure of rational elliptic spaces.

Abstract

For a rational elliptic space, this paper examines the relationship between its homotopy groups and its self-homotopy equivalence group. Moreover, we investigate how this group is embedded in general linear groups.