We show that the action of spacetime vector fields on variational bicomplex general relativity has a homotopy momentum map extends from to conserved currents given by Noether's first theorem morphism $L_\infty$-algebras.

In this paper, we introduce the notion of bicomplex partial metric space and prove some common fixed point theorems. The presented results generalize expand literature’s well-known results. An example application on is given.

In this paper, we derive an explicit group-invariant formula for the EulerLagrange equations associated with an invariant variational problem. The method relies on a group-invariant version of the variational bicomplex induced by a general equivariant moving frame construction, and is of independent interest. Mathematics Subject Classification (2000): Primary: 53A55, 58J70, 58E40 Secondary: 35A...

We conjecture an explicit formula for a cyclic analog of the Formality L∞-morphism [K]. We prove that its first Taylor component, the cyclic Hochschild-Kostant-Rosenberg map, is in fact a morphism (and a quasiisomorphism) of the complexes. To prove it we construct a cohomological version of the Connes-Tsygan bicomplex in cyclic homology. As an application of the cyclic Formality conjecture, we ...