Norms for compact Lie groups in equivariant stable homotopy theory

TL;DR

This paper develops a new construction of the relative norm in equivariant stable homotopy theory for compact Lie groups, extending previous work and connecting to equivariant factorization homology.

Contribution

It introduces an analogue of the Hill-Hopkins-Ravenel norm for compact Lie groups, generalizing existing constructions and utilizing a novel perspective via equivariant factorization homology.

Findings

Construction agrees with known norm for circle group

Explores properties of the new norm construction

Connects equivariant factorization homology with norm concepts

Abstract

We propose a construction of an analogue of the Hill-Hopkins-Ravenel relative norm $N_{H}^{G}$ in the context of a positive dimensional compact Lie group $G$ and closed subgroup $H$. We explore expected properties of the construction. We show that in the case when $G$ is the circle group (the unit complex numbers), the proposed construction here agrees with the relative norm constructed by Angeltveit, Gerhardt, Lawson, and the authors using the cyclic bar construction. Our construction is based on a new perspective on equivariant factorization homology, using framings to convert from actions of one group to another.