The topological cyclic Deligne conjecture

TL;DR

This paper proves that the totalization of a cyclic topological operad with multiplication admits an action of an operad equivalent to the framed little 2-discs operad, advancing the understanding of topological operad actions.

Contribution

It establishes a link between cyclic topological operads with multiplication and the framed little 2-discs operad using cosimplicial machinery.

Findings

Totalization of the cosimplicial space has an operad action

Connects cyclic topological operads to framed little 2-discs operad

Advances topological operad theory

Abstract

Let O be a cyclic topological operad with multiplication. In the framework of the cosimplicial machinery by McClure and Smith, we prove that the totalization of the cosimplicial space associated to O has an action of an operad equivalent to the framed little 2-discs operad.