Related papers: A Lefschetz fixed point theorem in gravitational l…
The theorem of Barth-Lefschetz is a statement about the cohomology of a submanifold X of some projective space, in a range depending on the codimension of the embedding. Here this is generalized to the case of a submanifold X of a smooth…
Recently we have proposed models of topological field theory including gravity in Mod. Phys. Lett. A 31 (2016) no.37, 1650213 and Phys. Rev. D 96 (2017) no.2, 024009, in order to solve the problem of the cosmological constant. The…
When light from a distant source object, like a galaxy or a supernova, travels towards us, it is deflected by massive objects that lie on its path. When the mass density of the deflecting object exceeds a certain threshold, multiple, highly…
In this paper we prove a tertiary index theorem which relates a spectral geometric and a homotopy theoretic invariant of an almost complex manifold with framed boundary. It is derived from the index theoretic and homotopy theoretic versions…
In this note we prove a more general (and topological) version of Gr\"unbaum's conjecture about affine invariant points. As an application of our result we show that, if we consider the action of the group of similarities, Gr\"unbaum's…
This paper is devoted to study the topological invariance of several non-uniform hyperbolicity conditions of one-dimensional maps. In contrast with the case of maps with only one critical point, it is known that for maps with several…
The Linearization Theorem for proper Lie groupoids organizes and generalizes several results for classic geometries. Despite the various approaches and recent works on the subject, the problem of understanding invariant linearization…
Complexifying space time has many interesting applications, from the construction of higher dimensional unification, to provide a useful framework for quantum gravity and to better define some local symmetries that suffer singularities in…
Topology in momentum space is the main characteristics of the ground states of a system at zero temperature, the quantum vacua. The gaplessness of fermions in bulk, on the surface or inside the vortex core is protected by topology.…
We revisit the question of whether the cosmological constant $\Lambda$ affects the cosmological gravitational bending of light, by numerical integration of the geodesic equations for a Swiss cheese model consisting of a point mass and a…
We propose a new theory of gravitation on noncommutative space-time which is invariant under the general coordinate transformations, while the local Lorentz invariance is realized as twisted gauge symmetry. Our theory is remarkably simpler…
An overview is given on those theoretical gravitational lensing results that can be formulated in a spacetime setting, without assuming that the gravitational fields are weak and that the bending angles are small. The first part is devoted…
For a Riemannian manifold $(M,g)$ with strictly convex boundary $\partial M$, the lens data consists in the set of lengths of geodesics $\gamma$ with endpoints on $\partial M$, together with their endpoints $(x_-,x_+)\in \partial M\times…
Our modified gravity theory (MOG) was used successfully in the past to explain a range of astronomical and cosmological observations, including galaxy rotation curves, the CMB acoustic peaks, and the galaxy mass power spectrum. MOG was also…
We investigate gravitational lensing in the context of the MOG modified theory of gravity. Using a formulation of the theory with no adjustable or fitted parameters, we present the MOG equations of motion for slow, nonrelativistic test…
The possible variation of the electromagnetic fine structure constant $\alpha_e$ on cosmological scales arouses great interests in recent years. The strongly lensed gravitational waves and the electromagnetic counterparts could be used to…
Microlensing studies are usually based on the lens equation that is valid only to the first order in the gravitational constant G and lens mass M. We consider corrections to the conventional lens equation in terms of differentiable…
The aim of the current paper is to study the multiscalar-tensor theories of gravity without derivative couplings. We construct a few basic objects that are invariant under a Weyl rescaling of the metric and transform covariantly when the…
Over the past decade advancements in the understanding of several astrophysical phenomena have allowed us to infer a concordance cosmological model that successfully accounts for most of the observations of our universe. This has opened up…
This paper presents new approaches to the fixed point property for nonexpansive mappings in L^1 spaces. While it is well-known that L^1 fails the fixed point property in general, we provide a complete and self-contained proof that…