Equivariant Framed Little Disk Operads are Additive

2024/10/26 by Szczesny, Ben
#55P48 (Secondary) #55P91 (Primary) 18M60 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2410.20235

Abstract

In this paper, we generalize the Dunn-Brinkmeier~additivity theorem, which establishes a weak equivalence C_n ⊗ C_m ≃ C_n+m for the little cubes operad 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.

Related

• Real models for the framed little n-disks operads
• Equivariant formality of the little disks operad
• On the additivity of the little cubes operads
• Operads and cosimplicial objects: an introduction
• A(nother) model for the framed little disks operad