相关论文: Natural vs. Artificial Topologies on a Relativisti…

We slightly extend the notion of a natural fibre bundle by requiring diffeomorphisms of the base to lift to automorphisms of the bundle only infinitesimally, i.e. at the level of the Lie algebra of vector fields. Spin structures are natural…

Given a time function $\tau$ on a spacetime $M$, we define a `null distance function', $\hat{d}_\tau$, built from and closely related to the causal structure of $M$. In basic models with timelike $\nabla \tau$, we show that 1)…

In this paper we establish a generally and globally valid coordinate system in curved space-time with the simultaneous hypersurface orthogonal to the time coordinate. The time coordinate can be preseted according to practical evolving…

We define a natural topology on the collection of (equivalence classes up to scaling of) locally finite measures on a homogeneous space and prove that in this topology, pushforwards of certain infinite volume orbits equidistribute in the…

In traditional topology optimization, the computing time required to iteratively update the material distribution within a design domain strongly depends on the complexity or size of the problem, limiting its application in real engineering…

The natural duality between "topological" and "regular," both considered as convergence space properties, extends naturally to p-regular convergence spaces, resulting in the new concept of a p-topological convergence space. Taking advantage…

The topology of orientable (2 + 1)d spacetimes can be captured by certain lumps of non-trivial topology called topological geons. They are the topological analogues of conventional solitons. We give a description of topological geons where…

The continuum has been one of the most controversial topics in mathematics since the time of the Greeks. Some mathematicians, such as Euclid and Cantor, held the position that a line is composed of points, while others, like Aristotle, Weyl…

Recently, there have been several applications of differential and algebraic topology to problems concerned with the global structure of spacetimes. In this paper, we derive obstructions to the existence of spin-Lorentz and pin-Lorentz…

The role of global topology in the dynamics of the Universe is poorly understood. Along with observational programmes for determining the topology of the Universe, some small theoretical steps have recently been made. Heuristic…

We extend the formalism of Topological T-duality to spaces which are the total space of a principal $S^1$-bundle $p:E \to W$ with an $H$-flux in $H^3(E,Z)$ together the together with an automorphism of the continuous-trace algebra on $E$…

Cosmological peculiar velocities have traditionally been studied within the framework of Newtonian theory. Around the turn of the century, a few quasi-Newtonian analyses appeared in the literature, but led to equations and results identical…

We provide five rearticulations of the thesis that the structure of spacetime is conventional, rather than empirically determined, based upon variation of the structures that are empirically underdetermined and modal contexts in which this…

Examples are given of the creation of closed timelike curves by choices of coordinate identifications. Following G\"odel's prescription, it is seen that flat spacetime can produce closed timelike curves with structure similar to that of…

All gauge theories need ``something fixed'' even as ``something changes.'' Underlying the implementation of these ideas all major physical theories make indispensable use of an elaborately designed spacetime model as the ``something…

The global topology of the Universe could, in principle, affect quantum systems through boundary condition constraints. We investigate this connection by analyzing how compact, flat, cosmologically inspired topologies, specifically the…

The family of topologies that induce the Euclidean metric space on every time axis and every space axis exhibits no maximal element when partially ordered by the relation ``finer than'', as demonstrated in this article. One conclusion and…

We investigate various classes of metrics on the integers, which induce the F\"urstenberg topology and establish the connection between the metrics and the topology. We analyze the norm-like mappings underlying these metrics, with respect…

Real topological phases protected by the spacetime inversion (P T) symmetry are a current research focus. The basis is that the P T symmetry endows a real structure in momentum space, which leads to Z2 topological classifications in 1D and…

We consider the quantization of space-times which can possess different topologies within a symmetry reduced version of Wheeler-DeWitt theory. The quantum states are defined from a natural decomposition as an outer-product of a topological…