Niveau: Supérieur, Doctorat, Bac+8
OPERADS OF NATURAL OPERATIONS I: LATTICE PATHS, BRACES AND HOCHSCHILD COCHAINS MICHAEL BATANIN, CLEMENS BERGER AND MARTIN MARKL Abstract. In this first paper of a series we study various operads of natural operations on Hochschild cochains and relationships between them. Contents 1. Introduction 1 2. The lattice path operad 2 3. Weak equivalences 6 4. Operads of natural operations 12 5. Operads of braces 20 Appendix A. Substitudes, convolution and condensation 26 References 29 1. Introduction This paper continues the efforts of [14, 3, 2] in which we studied operads naturally acting on Hochschild cochains of an associative or symmetric Frobenius algebra. A general approach to the operads of natural operations in algebraic categories was set up in [14] and the first breakthrough in computing the homotopy type of such an operad has been achieved in [3]. In [2], the same problem was approached from a combinatorial point of view, and a machinery which produces operads acting on the Hochschild cochain complex in a general categorical setting was introduced. However, some special instances of the construction of [2] are important in applications and have specific features not present in general. In this first paper of a series entitled ‘Operads of Natural Operations' we begin a detailed study of these special cases.
- points marked
- points equals
- decreasing map
- operads acting
- natural operations
- path operad
- unmarked
- lattice path