Positive weights and self-maps

TL;DR

This paper explores spaces with positive weights, demonstrating that finite complexes with such weights possess numerous self-maps and clarifying previous related results.

Contribution

It establishes the existence of many genuine self-maps in finite complexes with positive weights and corrects earlier proofs.

Findings

Finite complexes with positive weights have many self-maps.

Spaces with positive weights admit large families of automorphisms.

Previous related results are now rigorously proved.

Abstract

Spaces with positive weights are those whose rational homotopy type admits a large family of "rescaling" automorphisms. We show that finite complexes with positive weights have many genuine self-maps. We also fix the proofs of some previous related results.