The homotopy automorphisms of a marked n-stage

TL;DR

This paper investigates the properties of homotopy automorphisms of a marked n-stage in unstable coalgebras, establishing key nilpotency and completeness results that extend classical theories in algebraic topology.

Contribution

It introduces new nilpotency and completeness theorems for homotopy automorphisms of marked n-stages, expanding the understanding of their role in the moduli problem of unstable coalgebras.

Findings

Proves nilpotency of homotopy automorphisms.

Establishes completeness results for these automorphisms.

Extends classical results by Dror, Zabrodsky, Maruyama, and Møller.

Abstract

We show nilpotency and completeness results for the homotopy automorphisms of a marked n-stage for an unstable coalgebra. These objects figure in the moduli problem of unstable coalgebras. Our theorems extend classical work of Dror, Zabrodsky, Maruyama and M\o ller.