Equivariant Framed Little Disk Operads are Additive

Abstract

In this paper, we generalize the Dunn-Brinkmeier~additivity theorem, which establishes a weak equivalence ${\mathcal{C}}_n\otimes {\mathcal{C}}_m\simeq {\mathcal{C}}_{n+m}$ for the little cubes operad ${\mathcal{C}}_n$. We introduce equivariant framed little disk operads, a new class of operads that simultaneously generalize the framed little disk operads and the little $V$-disk operads associated with a $G$-representation $V$. We prove that these operads satisfy an analogous additivity property, extending the classical theorem to settings involving group actions and framings.

62 pages. Comments and feedback welcome