Unstable Adams operations acting on $p$-local compact groups and fixed points

TL;DR

This paper demonstrates that p-local compact groups can be approximated by finite p-group transporter systems using unstable Adams operations, analyzing the structure of fixed points to establish this connection.

Contribution

It introduces a method to approximate p-local compact groups with finite p-group transporter systems via unstable Adams operations and fixed point analysis.

Findings

p-local compact groups are approximated by finite p-group transporter systems

unstable Adams operations help analyze fixed points in these groups

provides a new approach to understanding the structure of p-local compact groups

Abstract

We prove in this paper that every $p$-local compact group is approximated by transporter systems over finite $p$-groups. To do so, we use unstable Adams operations acting on a given $p$-local compact group and study the structure of resulting fixed points.