Global transfer systems of abelian compact Lie groups

TL;DR

This paper classifies all global transfer systems for abelian compact Lie groups, providing a comprehensive understanding of their structure in globally equivariant homotopy theory.

Contribution

It explicitly describes and completely classifies global transfer systems for all abelian compact Lie groups, linking them to global $N_ abla$-operads.

Findings

Complete classification of global transfer systems for abelian compact Lie groups

Connection between transfer systems and levels of commutativity in equivariant homotopy theory

Explicit description of the structure of these transfer systems

Abstract

Global transfer systems are equivalent to global $N_\infty$-operads, which parametrize different levels of commutativity in globally equivariant homotopy theory, where objects have compatible actions by all compact Lie groups. In this paper we explicitly describe and completely classify global transfer systems for the family of all abelian compact Lie groups.