Fibrations of classifying spaces in the simplicial setting

TL;DR

This paper demonstrates that in the simplicial setting, the classifying space construction transforms short exact sequences of groups into fiber bundles, strengthening the connection from homotopy fibrations to actual fiber bundles.

Contribution

It establishes that classifying space construction in the simplicial context yields fiber bundles from short exact sequences, not just homotopy fibrations, enhancing the understanding of their topological structure.

Findings

Classifying space construction converts short exact sequences into fiber bundles.

Strengthens the link between algebraic sequences and topological fiber structures.

Provides a new perspective on the topological realization of algebraic data.

Abstract

In this note we show that in the simplicial setting, the classifying space construction converts short exact sequences of groups not just to homotopy fibrations, but in fact to fibre bundles.