In this paper, we construct groupoid coloured operads governing props and wheeled props,
and show they are Koszul. This is accomplished by new biased definitions for (wheeled) …

Circuit algebras, used in the study of finite-type knot invariants, are a symmetric analogue of
Jones's planar algebras. This work, the first of a pair of papers comprising a detailed study of …

Circuit algebras originated in quantum topology and are a symmetric analogue of Jones's
planar algebras. This paper is the second of a pair that together provide detailed conceptual …

This work presents a detailed analysis of the combinatorics of modular operads. These are
operad-like structures that admit a contraction operation as well as an operadic …

Circuit algebras, used in the study of finite-type knot invariants, are a symmetric analogue of
Jones's planar algebras. They are very closely related to circuit operads, which are a …

In [Math. Ann. 367 (2017), pp. 1517–1586] Bar-Natan and the first author show that solutions
to the Kashiwara–Vergne equations are in bijection with certain knot invariants …

We recall several categories of graphs which are useful for describing homotopy-coherent
versions of generalised operads (eg cyclic operads, modular operads, properads, and so …

We explain a direct topological proof for the multiplicativity of the Duflo isomorphism for
arbitrary finite-dimensional Lie algebras, and derive the explicit formula for the Duflo map …

We show that solutions to the Kashiwara-Vergne problem can be extended degree by
degree. This can be used to simplify the computation of a class of Drinfel'd associators …

Homomorphic expansions are combinatorial invariants of knotted objects, which are
universal in the sense that all finite-type (Vassiliev) invariants factor through them …