Lifting $N_\infty$ operads from conjugacy data

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 $\operatorname{Sub}(G)/G$.Comment: v2: updates in response to referee report, accepted version in Tunisian Journal of Mathematics; 24 pages, 16 figures. v1: 22 pages, 13 figures; comments welcome