On the group of self-homotopy equivalences of an $F_{0}$-Space

TL;DR

This paper proves G. Lupton's conjecture that the group of self-homotopy equivalences of an $F_0$-space inducing the identity on homotopy groups is finite, advancing understanding in algebraic topology.

Contribution

The paper establishes the finiteness of the group of self-homotopy equivalences of an $F_0$-space that induce the identity on homotopy groups, confirming a conjecture by G. Lupton.

Findings

Proves the finiteness of the specified group of self-homotopy equivalences.

Confirms G. Lupton's conjecture in the context of $F_0$-spaces.

Advances theoretical understanding of homotopy equivalences in algebraic topology.

Abstract

In \cite{G}, G. Lupton conjectured that the group of self-homotopy equivalences of an $F_0$-space inducing the identity on the homotopy groups is finite. Thus, the aim of this paper is to establish this conjecture.