A compactification of the real configuration space as an operadic completion (Q1291106)

Let \(C_{n}^{0}(V)\) denote the configuration space of \(n\)-tuples of distinct points in \(V\). If \(V\) is a compact Riemannian manifold there exists a compactification of \(C_{n}^{0}(V)\) denoted by \(C_{n}(V)\), due to \textit{S. Axelrod} and \textit{I. M. Singer} [J. Differ. Geom 39, No. 1, 173-213 (1994; Zbl 0827.53057)]. There is a similar compactification of the moduli space of configuations of \(n\)-tuples of distinct points in \({\mathbb R}^{n}\) modulo the action of the affine group. In this paper the author introduces the notion of partial operads and their partial modules. An operation of operad completion is defined for these structures and the compactifications mentioned above are shown to be constructible as such operad completions.