Related papers: Detecting Causality with Symplectic Quandles
A classical result in Lorentzian geometry states that a strongly causal spacetime is globally hyperbolic if and only if the Lorentzian distance is finite valued for every metric choice in the conformal class. It is proven here that a…
We prove an analog of Shilnikov Lemma for a normally hyperbolic symplectic critical manifold $M\subset H^{-1}(0)$ of a Hamiltonian system. Using this result, trajectories with small energy $H=\mu>0$ shadowing chains of homoclinic orbits to…
Recent work shows that causal facts can be effectively extracted from LLMs through prompting, facilitating the creation of causal graphs for causal inference tasks. However, it is unclear if this success is limited to explicitly-mentioned…
The notion of special symplectic connections is closely related to contact parabolic geometries due to the work of M. Cahen and L. Schwachh\"ofer. We remind their characterization and reinterpret the result in terms of generalized Weyl…
We describe a relation between Arnold's strange duality and a polar duality between the Newton polytopes which is mostly due to M.~Kobayashi. We show that this relation continues to hold for the extension of Arnold's strange duality found…
Causality is fundamental to science, but it appears in several different forms. One is relativistic causality, which is tied to a space-time structure and forbids signalling outside the future. A second is an operational notion of causation…
We create a framework for odd Khovanov homology in the spirit of Bar-Natan's construction for the ordinary Khovanov homology. Namely, we express the cube of resolutions of a link diagram as a diagram in a certain 2-category of chronological…
A symplectic manifold $W$ with contact type boundary $M = \partial W$ induces a linearization of the contact homology of $M$ with corresponding linearized contact homology $HC(M)$. We establish a Gysin-type exact sequence in which the…
The transition maps for a Sobolev $G$-bundle are not continuous in the critical dimension and thus the usual notion of topology does not make sense. In this work, we show that if such a bundle $P$ is equipped with a Sobolev connection $A$,…
Stringent limits on the Myers-Pospelov timelike parameter for photons $\xi<10^{-15}$ coming from astrophysical tests suggest exploring more general preferred backgrounds, such as spacelike and lightlike. We take some steps in this…
Nowadays, the need for causal discovery is ubiquitous. A better understanding of not just the stochastic dependencies between parts of a system, but also the actual cause-effect relations, is essential for all parts of science. Thus, the…
The Groups of causal and conformal automorphisms of globally hyperbolic spacetimes were studied. In two dimensions, we prove that all globally hyperbolic spacetimes that are directed and connected are causally isomorphic. We work out the…
We address the problem of estimating causal effects from observational data in the presence of network confounding, a setting where both treatment assignment and observed outcomes of individuals may be influenced by their neighbors within a…
We develop an appropriate dihedral extension of the Connes-Moscovici characteristic map for Hopf *-algebras. We then observe that one can use this extension together with the dihedral Chern character to detect non-trivial $L$-theory classes…
In this paper, we explore the bounded cohomology of quandles and its applications to knot theory. We establish two key results that provide sufficient conditions for the infinite dimensionality of the second bounded cohomology of quandles.…
Systems in which exchange interactions couple carrier spins to a spin texture with a net chirality exhibit a spin-dependent Aharonov-Bohm effect, where the geometric gauge field and pseudo-magnetic field have opposite signs for carriers…
A unifying framework for the study of causal relations is presented. The causal relations are regarded as subsets of M x M and the role of the corresponding antisymmetry conditions in the construction of the causal ladder is stressed. The…
A number of techniques in Lorentzian geometry, such as those used in the proofs of singularity theorems, depend on certain smooth coverings retaining interesting global geometric properties, including causal ones. In this note we give…
A hierarchy of multimode uncertainty relations on the second moments of n pairs of canonical operators is derived in terms of quantities invariant under linear canonical (i.e. symplectic) transformations. Conditions for the separability of…
General Relativity in 4 dimensions can be equivalently described as a dynamical theory of SO(3)-connections rather than metrics. We introduce the notion of asymptotically hyperbolic connections, and work out an analog of the…