Related papers: On two chain models for the gravity operad
We review several well-known operads of compactified configuration spaces and construct several new such operads, C, in the category of smooth manifolds with corners whose complexes of fundamental chains give us (i) the 2-coloured operad of…
I describe a bi-connection formalism of General relativity based on the dual role of the Weitzenb\"{o}ck connection defining the parallelism at a distance and the concomitant Levi-Civita connection derived from the Riemannian metric. A more…
It is shown how some results on harmonic maps within the chiral model can be carried over to self-dual gravity. The WZW-like action for self-dual gravity is found.
This note is a complement to Pusz--Woronowicz's works on functional calculus for two positive forms from the viewpoint of operator theory. Based on an elementary, self-contained and purely Hilbert space operator explanation of their…
We construct a space of string diagrams, which are a type of fatgraph with some additional data, and show that there are string topology operations on the chains of the free loop space of a closed Riemannian manifold which are parameterized…
We look for a classical double copy structure between gravity and electrodynamics by connecting the descriptions of the scattering of two point masses, and of two point charges, in terms of perturbative (post-Minkowskian or post-Lorentzian)…
We review the main tools which allow for the statistical characterization of weighted networks. We then present two case studies, the airline connection network and the scientific collaboration network, which are representative of critical…
In the works of A. Ach\'ucarro and P. K. Townsend and also by E. Witten, a duality between three-dimensional Chern-Simons gauge theories and gravity was established. In all cases, the results made use of the field equations. In a previous…
Working in the first order formalism of gravity, we propose an action that combines the self and anti-self-dual parts of the curvature and comprises all the diffeomorphism invariant Lagrangians that one can consider in this formalism. The…
We study two closely related operads: the Gelfand-Dorfman operad GD and the Conformal Lie Operad CLie. The latter is the operad governing the Lie conformal algebra structure. We prove Koszulity of the Conformal Lie operad using the Groebner…
We show that as in the case of isotropic models, the `Dirac Algorithm' and `Modified Horowitz' Formalism' lead to identical phase-space structure of the Hamiltonian for the gravitational action with curvature squared terms, in anisotropic…
We compare two different constructions of higher dimensional parallel transport. On the one hand, there is the two dimensional parallel transport associated to 2-connections on 2-bundles studied by Baez-Schreiber, Faria Martins-Picken and…
In the last few decades, extensions of General Relativity have reached always more attention especially in view of possible breakdowns of the standard $\Lambda$CDM paradigm at intermediate and high redshift regimes. If General Relativity…
It is clarified how cohomologies and Gerstenhaber algebras can be associated with linear pre-operads (comp algebras). Their relation to mechanics and operadic physics is concisely discussed.
The purpose of this paper is to establish some neccessary and sufficient conditions for the boundedness of a general class of multilinear Hausdorff operators that acts on the product of some two weighted function spaces such as the two…
Topological euclidean gravity is built in eight dimensions for manifolds with $Spin(7) \subset SO(8)$ holonomy. In a previous work, we considered the construction of an eight-dimensional topological theory describing the graviton and one…
We discuss a Randall-Sundrum-type two D-braneworld model in which D-branes possess different values of the tensions from those of the charges, and derive an effective gravitational equation on the branes. As a consequence, the…
We show that excitations of physical interest of the heavenly equation are generated by symmetry operators which yields two reduced equations with different characteristics. One equation is of the Liouville type and gives rise to…
In this paper, we prove that given two cubical links of dimension two in ${\mathbb R}^4$, they are isotopic if and only if one can pass from one to the other by a finite sequence of cubulated moves. These moves are analogous to the…
We propose a model of gravity in which a General Relativity metric tensor and an effective metric generated from a single scalar formulated in Geometric Scalar Gravity are mixed. We show that the model yields the exact Schwarzschild…