UCLA

In this dissertation, we investigate equivariant generalisations of Dunn Additivity. We first build equivariant operads called little star operads, which encompass little cube and little disk operads and prove they provide models of $\mathbb{E}_V$-operads. We then show general conditions for when additivity holds for these operads. In particular, we prove that an equivariant additivity theorem holds for simplex-shaped operads. We then consider another operad construction aimed to model more general $\mathbb{N}$-operads. We show that while they provide an approximation for $\mathbb{N}_\infty$-operads, they seem to fail a corresponding additivity theorem.