Classifying spaces of compact Lie groups that are p-compact for all prime numbers

TL;DR

This paper investigates conditions under which the classifying space of a compact Lie group is p-compact for all primes, focusing on subgroups of simple Lie groups and including a survey of p-compactness at a single prime.

Contribution

It characterizes when the classifying space of a compact Lie group is p-compact for all primes, especially for subgroups of simple Lie groups, and surveys p-compactness at individual primes.

Findings

Identifies conditions for p-compactness of classifying spaces across all primes.

Provides a classification for subgroups of simple Lie groups with p-compact classifying spaces.

Includes a comprehensive survey of p-compactness at a single prime.

Abstract

We consider a problem on the conditions of a compact Lie group G that the loop space of the p-completed classifying space be a p-compact group for a set of primes. In particular, we discuss the classifying spaces BG that are p-compact for all primes when the groups are certain subgroups of simple Lie groups. A survey of the p-compactness of BG for a single prime is included.