# Cellular approximations of p-local compact groups

## TL;DR

This paper computes cellular approximations of classifying spaces of p-local compact groups, especially those related to compact Lie groups, using the framework of A-cellular approximation.

## Contribution

It provides explicit calculations of A-cellular approximations for classifying spaces of p-local compact groups, extending the understanding of their homotopical properties.

## Key findings

- Explicit A-cellular approximations for classifying spaces of p-local compact groups.
- Special focus on cases from compact Lie groups.
- Enhanced understanding of the homotopy theory of p-local groups.

## Abstract

Let A be the classifying space of an abelian p-torsion group. We compute A-cellular approximations (in the sense of Chach\'olski and Farjoun) of classifying spaces of p-local compact groups, with special emphasis in the cases which arise from honest compact Lie groups.