Overlapping Discs Filtration in the Commutative Operad

TL;DR

This paper investigates the structure of configuration spaces of non-overlapping discs as a filtered operad and explores the induced homology structure, advancing understanding of operadic and topological properties.

Contribution

It introduces a new analysis of the filtered operad structure of non-overlapping discs configuration spaces and examines the homology induced by this structure.

Findings

Spaces form a filtered operad

Homology inherits a related algebraic structure

Provides new insights into operadic topology

Abstract

The spaces of configurations of non-$k$-overlapping discs have been studied as a bimodule over the little discs operad. In fact, the spaces form a filtered operad. We define and study the induced structure on the homology.