Models for the n-Swiss Cheese operads

TL;DR

This paper develops combinatorial Hopf (co-)operadic models for the Swiss Cheese operads using Feynman diagrams, extending earlier models for the little disks operads by Kontsevich and Lambrechts-Volić.

Contribution

It introduces new combinatorial models for Swiss Cheese operads based on Feynman diagrams, expanding the framework of operadic models.

Findings

Constructed explicit Hopf (co-)operadic models for Swiss Cheese operads.

Extended the existing models from little disks to Swiss Cheese operads.

Provides a combinatorial approach to operad modeling.

Abstract

We describe combinatorial Hopf (co-)operadic models for the Swiss Cheese operads built from Feynman diagrams. This extends previous work of Kontsevich and Lambrechts-Voli\'c for the little disks operads.