Operads, operadic categories and the blob complex

Abstract

We will show that the Morrison-Walker blob complex appearing in Topological Quantum Field Theory is an operadic bar resolution of a certain operad composed of fields and local relations. As a by-product we develop the theory of unary operadic categories and study some novel and interesting phenomena arising in this context.

Figures (4)

• Figure 1: A piece of the colored operad ${\EuScript {F\!}_c}$ -- a schematic picture of a 'punctured blob.'
• Figure 2: Viewing elements of $B_*({\EuScript M}_c,{\EuScript {F\!}_c},{\EuScript I}_c)(\emptyset)$ as forests. Internal vertices are decorated by fields on punctured blobs, leaves by generators of local relations, the soil by a field on ${\mathbb M}$.
• Figure 3: The initial part of the augmented bar construction.
• Figure 4: Sundry chain complexes and their maps.

Theorems & Definitions (111)

• Remark 1
• Lemma 2
• proof
• Definition 3
• Definition 4
• Remark 5
• Lemma 6
• proof
• Corollary 7
• proof