Related papers: On two chain models for the gravity operad

Let $\overline{\mathcal{M}}_{0,n+1}$ be the moduli space of genus zero stable curves with $(n+1)$-marked points. The collection $\overline{\mathcal{M}}=\{\overline{\mathcal{M}}_{0,n+1}\}_{n\geq 2}$ forms an operad in the category of complex…

We show that Willwacher's cyclic formality theorem can be extended to preserve natural Gravity operations on cyclic multivector fields and cyclic multidifferential operators. We express this in terms of a homotopy Gravity quasi-isomorphism…

First we argue that many BV and homotopy BV structures, including both familiar and new examples, arise from a common underlying construction. The input of this construction is a cyclic operad along with a cyclically invariant Maurer-Cartan…

Based on operator identities and their formal adjoints, we derive two symmetry operators for the linearized Einstein operator on vacuum backgrounds of Petrov type D and in particular the Kerr spacetime. One of them is of differential order…

A model of two--dimensional gravity with an action depending only on a linear connection is considered. This model is a topological one, in the sense that the classical action does not contain a metric or zweibein at all. A metric and an…

It is shown that the action for topological gravity in even dimensions is, except by a multiplicative constant, a gauged Wess-Zumino-Witten Term.

We study the class of hyponormal 2-variable weighted shifts with two consecutive equal weights in the weight sequence of one of the coordinate operators. We show that under natural assumptions on the coordinate operators, the presence of…

Ostrogradsky's, Dirac's and Horowitz's techniques of higher order theories of gravity produce identical phase-space structures. The problem is manifested in the case of Gauss-Bonnet-dilatonic coupled action in the presence of higher-order…

From an operad C with an action of a group G, we construct new operads using the homotopy fixed point and orbit spectra. These new operads are shown to be equivalent when the generalized G-Tate cohomology of C is trivial. Applying this…

The class of Zeeman topologies on spacetimes in the frame of relativity theory is considered to be of powerful intuitive justification, satisfying a sequence of properties with physical meaning, such as the group of homeomorphisms under…

We prove that two chains of linear mappings are topologically isomorphic if and only if they are linearly isomorphic.

In this paper a topological theory of gravity is studied on a four-manifold using the formalism of Capovilla {\sl et al}. We show that it is fact equivalent to Anselmi and Fre's topological gravity using the topological symmetries. Using…

We define a construction on operads which yields a new description of the minimal model. The construction also allows us to define algebraic structures on the homology of chain complexes with homologously trivial operad algebra structures,…

Given a space with a circle action, we study certain cocyclic chain complexes and prove a theorem relating cyclic homology to $S^1$-equivariant homology, in the spirit of celebrated work of Jones. As an application, we describe a chain…

The notion of an upward plane graph in graph theory and that of a progressive plane graph (or plane string diagram) in category theory are essentially the same thing. In this paper, we combine the ideas in graph theory and category theory…

The chain gravity properad introduced earlier by the author acts on the cyclic Hochschild of any cyclic $A_\infty$ algebra equipped with a scalar product of degree $-d$. In particular, it acts on the cyclic Hochschild complex of any…

A chain complex model for the free loop space of a connected, closed and oriented manifold is presented, and on its homology, the Gerstenhaber and Batalin-Vilkovisky algebra structures are defined and identified with the string topology…

We extend Padmanabhan's entropy functional formalism to show that, in addition to the Gauss-Bonnet or the entire series of Lanczos-Lovelock Lagrangians already obtained, more general higher-order corrections to General Relativity, i.e., the…

We show that any two diagrams of the same knot or link are connected by a sequence of Reidemeister moves which are sorted by type.

We compute the structure of the homology of an operad built from the spaces TH_{d,n} of configurations of points in C^d, modulo translation and homothety. We find that it is a mild generalization of Getzler's gravity operad, which occurs in…