Operads of moduli spaces of points in C^d

TL;DR

This paper analyzes the homology of an operad formed from configuration spaces of points in complex d-dimensional space, revealing a generalization of Getzler's gravity operad for higher dimensions.

Contribution

It computes the homology of a new operad related to point configurations in C^d, extending known structures from the one-dimensional case.

Findings

Homology of the operad is a mild generalization of Getzler's gravity operad.

The structure is explicitly computed for spaces of points in C^d.

The results connect configuration spaces with operad theory in higher dimensions.

Abstract

We compute the structure of the homology of an operad built from the spaces TH_{d,n} of configurations of points in C^d, modulo translation and homothety. We find that it is a mild generalization of Getzler's gravity operad, which occurs in dimension d = 1.