Computing Homotopy Types Using Crossed N-Cubes of Groups

TL;DR

This paper discusses algebraic structures derived from groupoids that enable explicit and computable descriptions of homotopy n-types, offering advantages over traditional models like Postnikov systems.

Contribution

It introduces algebraic descriptions of homotopy n-types using crossed N-cubes of groups, providing explicit and computable models distinct from classical approaches.

Findings

Algebraic models for homotopy n-types are explicitly constructed.

These models are more computationally accessible than traditional methods.

The approach offers new tools for understanding homotopy types.

Abstract

The aim of this paper is to explain how, through the work of a number of people, some algebraic structures related to groupoids have yielded algebraic descriptions of homotopy n-types. Further, these descriptions are explicit, and in some cases completely computable, in a way not possible with the traditional Postnikov systems, or with other models, such as simplicial groups.