Related papers: Gluing constructions for Lorentzian length spaces
The notion of gluing of abelian categories was introduced by Kazhdan and Laumon in an attempt of another geometric construction of representations of finite Chevalley groups; the approach was later developed by Polishchuk and Braverman. We…
Recent advances in the theory of metric measures spaces on the one hand, and of sub-Riemannian ones on the other hand, suggest the possibility of a "great unification" of Riemannian and sub-Riemannian geometries in a comprehensive framework…
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…
We develop a method of gluing the local mirrors and functors constructed from immersed Lagrangians in the same deformation class. As a result, we obtain a global mirror geometry and a canonical mirror functor. We apply the method to…
We study generalizations of Lorentzian warped products with one-dimensional base of the form $I\times_f X$, where $I$ is an interval, $X$ is a length space and $f$ is a positive continuous function. These generalized cones furnish an…
An important, if relatively less well known aspect of the singularity theorems in Lorentzian Geometry is to understand how their conclusions fare upon weakening or suppression of one or more of their hypotheses. Then, theorems with modified…
The definitions of global hyperbolicity for closed cone structures and topological preordered spaces are known to coincide. In this work we clarify the connection with definitions of global hyperbolicity proposed in recent literature on…
Classical Kleinian groups are discrete subgroups of isometries of H n. The well-known theory of Kleinian groups starts with the definition of their associated limit set in the boundary of H n , and includes the geometric properties of the…
In this paper, we prove the rationality of the gluing relation of edge replacement systems, which were introduced for studying rearrangement groups of fractals. More precisely, we describe an algorithmic procedure for building a finite…
In this paper, we study complete space-like $\lambda$-hypersurfaces in the Lorentzian space $\mathbb R^{n+1}_1$. As the result, we prove some rigidity theorems for these hypersurfaces including the complete space-like self-shrinkers in…
It is demonstrated that any two reference frames (RFs), which are uniformly and rectilinearly moving relative to each other, can be adjusted via (possibly anisotropic) rescaling and re-synchronization so that the resulting pair of RFs is…
The configuration space of general relativity is superspace - the space of all Riemannian 3-metrics modulo diffeomorphisms. However, it has been argued that the configuration space for gravity should be conformal superspace - the space of…
We use a construction which we call generalized cylinders to give a new proof of the fundamental theorem of hypersurface theory. It has the advantage of being very simple and the result directly extends to semi-Riemannian manifolds and to…
We prove that there are no restrictions on the spatial topology of asymptotically flat solutions of the vacuum Einstein equations in (n+1)-dimensions. We do this by gluing a solution of the vacuum constraint equations on an arbitrary…
We present the notion of temporal Lorentzian spectral triple which is an extension of the notion of pseudo-Riemannian spectral triple with a way to ensure that the signature of the metric is Lorentzian. A temporal Lorentzian spectral triple…
We construct examples of compact and one-ended constant mean curvature surfaces with large mean curvature in Riemannian manifolds with axial symmetry by gluing together small spheres positioned end-to-end along a geodesic. Such surfaces…
Using punctual gluing of $t$-structures, we construct an analogue of S. Morel's weight truncation functors (for certain weight profiles) in the setting of motivic sheaves. As an application we construct a canonical motivic analogue of the…
We describe applications of the gluing formalism discussed in the companion paper. When a $d$-dimensional local theory $\text{QFT}_d$ is supersymmetric, and if we can find a supersymmetric polarization for $\text{QFT}_d$ quantized on a…
The straightening-unstraightening correspondence of Grothendieck--Lurie provides an equivalence between cocartesian fibrations between $(\infty, 1)$-categories and diagrams of $(\infty, 1)$-categories. We provide an alternative proof of…
We apply Cartan's method of equivalence to construct invariants of a given null hypersurface in a Lorentzian space-time. This enables us to fully classify the internal geometry of such surfaces and hence solve the local equivalence problem…