Bousfield-Kan completion and very large groups

TL;DR

This paper develops new criteria for determining the $R$-badness of spaces and applies these criteria specifically to closed surfaces, advancing understanding in algebraic topology.

Contribution

It introduces novel criteria for $R$-badness and demonstrates their application to the case of closed surfaces, providing new insights.

Findings

New criteria for $R$-badness of spaces

Application of criteria to closed surfaces

Enhanced understanding of Bousfield-Kan completion

Abstract

We establish new criteria for the $R$-badness of a space and apply it to the case of closed surfaces.