Classifying Space via Homotopy Coherent Nerve

TL;DR

This paper demonstrates that the classifying space of a simplicial group can be accurately modeled using its homotopy coherent nerve, bridging a gap between algebraic and topological models.

Contribution

It establishes a new equivalence between the classifying space of a simplicial group and its homotopy coherent nerve, providing a novel modeling approach.

Findings

Classifying space is modeled by homotopy coherent nerve.

Provides a new algebraic-topological correspondence.

Enhances understanding of simplicial groups and their classifying spaces.

Abstract

We prove that the classifying space of a simplicial group is modeled by its homotopy coherent nerve.