Lifting $N_\infty$ operads from conjugacy data

TL;DR

This paper introduces 'lossless groups' and establishes a correspondence between homotopy classes of $N_ abla$ operads and specific transfer systems based on conjugacy classes, advancing understanding in equivariant operad theory.

Contribution

It defines lossless groups and links $N_ abla$ operads to transfer systems, providing a new classification framework in equivariant homotopy theory.

Findings

Lossless groups are characterized and isolated.

Homotopy classes of $N_ abla$ operads correspond to restricted transfer systems.

The correspondence simplifies the classification of $N_ abla$ operads.

Abstract

We isolate a class of groups -- called lossless groups -- for which homotopy classes of $G$-$N_\infty$ operads are in bijection with certain restricted transfer systems on the poset of conjugacy classes $\operatorname{Sub}(G)/G$.