Related papers: Do Link Polynomials Detect Causality In Globally H…
We consider knots and links in handlebodies that have hyperbolic complements and operations akin to composition. Cutting the complements of two such open along separating twice-punctured disks such that each of the four resulting…
To clarify some aspects of the application of Special Relativity, spacetime is sliced into null geodesic hypersurfaces as an alternative to the hypersurfaces of simultaneity normally adopted. Events at particle locations on the hypersurface…
All three-manifolds are known to occur as Cauchy surfaces of asymptotically flat vacuum spacetimes and of spacetimes with positive-energy sources. We prove here the conjecture that general relativity does not allow an observer to probe the…
The expression of causality depends on an underlying choice of chronology. Since a chronology is provided by any Lorentzian metric in relativistic theories, there are as many expressions of causality as there are non-conformally related…
For smooth families with maximal variation, whose general fibers have semi-ample canonical bundle, the generalized Viehweg hyperbolicity conjecture states that the base spaces of such families are of log general type. This deep conjecture…
In this work we provide the full description of the upper levels of the classical causal ladder for spacetimes in the context of Lorenztian length spaces, thus establishing the hierarchy between them. We also show that global hyperbolicity,…
This monograph derives direct and concrete relations between colored Jones polynomials and the topology of incompressible spanning surfaces in knot and link complements. Under mild diagrammatic hypotheses that arise naturally in the study…
It is shown that a spacetime with collisionless matter evolving from data on a compact Cauchy surface with hyperbolic symmetry can be globally covered by compact hypersurfaces on which the mean curvature is constant and by compact…
Recently many people have discussed the possibility that the universe is hyperbolic and was in an inflationary phase in the early stage. Under these assumptions, it is shown that the universe cannot have compact hyperbolic time-slices.…
We construct and identify star representations canonically associated with holonomy reducible simple symplectic symmetric spaces. This leads the a non-commutative geometric realization of the correspondence between causal symmetric spaces…
We formulate an algebraic criterion for the presence of global anomalies on globally hyperbolic space-times in the framework of locally covariant field theory. We discuss some consequences and check that it reproduces the well-known global…
Quotients $Y=X/conj$ of complex surfaces by anti-holomorphic involutions $conj\: X\to X$ tend to be completely decomposable when they are simply connected, i.e., split into connected sums, $n CP^2\#m\barCP2$, if $w_2(Y)\ne0$, or into…
Causality is pivotal to our understanding of the world, presenting itself in different forms: information-theoretic and relativistic, the former linked to the flow of information, the latter to the structure of space-time. Leveraging a…
Khovanov homology is an invariant for links in the three sphere that categorizes the Jones polynomial. We extend Khovanov's construction to links in 3-manifolds that are connected sums of orientable interval bundles over surfaces. Cutting…
We consider how causality and micro-causality are realised in QED in curved spacetime. The photon propagator is found to exhibit novel non-analytic behaviour due to vacuum polarization, which invalidates the Kramers-Kronig dispersion…
We consider globally hyperbolic spacetimes with compact Cauchy surfaces in a setting compatible with the presence of a positive cosmological constant. More specifically, for 3+1 dimensional spacetimes which satisfy the null energy condition…
A novel approach is developed for discovering directed connectivity between specified pairs of nodes in a high-dimensional network (HDN) of brain signals. To accurately identify causal connectivity for such specified objectives, it is…
In 1983, Conway and Gordon proved that for every spatial complete graph on six vertices, the sum of the linking numbers over all of the constituent two-component links is odd, and that for every spatial complete graph on seven vertices, the…
Some results related to the causality of compact Lorentzian manifolds are proven: (1) any compact Lorentzian manifold which admits a timelike conformal vector field is totally vicious, and (2) a compact Lorentzian manifold covered regularly…
In this article we present a review of a geometric and algebraic approach to causal cones and describe cone preserving transformations and their relationship with the causal structure related to special and general relativity. We describe…