Vertex partial operads

Abstract

In Chapters 1 and 3, the moduli spaces K(n), n ∈ ℕ, and the sewing operation are denned and studied. In this chapter we study the sequence

$$K = {\left\{ {K(n)} \right\}_{n \in \mathbb{N}}}$$

from the viewpoint of the theory of operads. For a brief introduction to the basic notions in the theory of operads and partial operads, see Appendix C and the references there. We show that K has a natural structure of an analytic associative ℂ^×-rescalable partial operad (see Appendix C for the definition). The most natural analytic structures on K(n), n ∈ ℕ, are structures of (LB)-manifolds denned in Appendix B. The partial operad K is called the “sphere partial operad.”