Related papers: On 4-dimensional Lorentz-structures, Dark energy a…
Two questions on the topology of compact energy surfaces of natural two degrees of freedom Hamiltonian systems in a magnetic field are discussed. We show that the topology of this 3-manifold (if it is not a unit tangent bundle) is uniquely…
The topological theory of phase transitions was proposed on the basis of different arguments, the most important of which are: a direct evidence of the relation between topology and phase transitions for some exactly solvable models; an…
The relation between thermodynamic phase transitions in classical systems and topology changes in their configuration space is discussed for a one-dimensional, analytically tractable solid-on-solid model. The topology of a certain family of…
We show that any closed oriented 3-manifold can be topologically embedded in some simply-connected closed symplectic 4-manifold, and that it can be made a smooth embedding after one stabilization. As a corollary of the proof we show that…
We construct series of examples of exotic smooth structures on compact locally symmetric spaces of noncompact type. In particular, we obtain higher rank examples, which do not support Riemannian metric of nonpositive curvature. The examples…
Since the first work on exotic smoothness in physics, it was folklore to assume a direct influence of exotic smoothness to quantum gravity. Thus, the negative result of Duston (arXiv:0911.4068) was a surprise. A closer look into the…
Under the existence of a massless spinor with respect to the total connection in a spacetime modeled as a Lorentzian manifold with internal boundaries, such as finite volume semi-classical Black Holes, we show that a topological mechanism…
The essential role played by differentiable structures in physics is reviewed in light of recent mathematical discoveries that topologically trivial space-time models, especially the simplest one, ${\bf R^4}$, possess a rich multiplicity of…
We show how to construct absolutely exotic smooth structures on compact 4-manifolds with boundary, including contractible manifolds. In particular, we prove that any compact smooth 4-manifold W with boundary that admits a relatively exotic…
We show that a topology can be defined in the four dimensional space-time of special relativity so as to obtain a topological semigroup for time. The Minkowski 4-vector character of space-time elements as well as the key properties of…
The topological charge is constructed for SU(3) center vortex world-surfaces composed of elementary squares on a hypercubic lattice. In distinction to the SU(2) case investigated previously, it is necessary to devise a proper treatment of…
We connect topological changes that can occur in $3$-space via surgery, with black hole formation, the formation of wormholes and new generalizations of these phenomena, including relationships between quantum entanglement and wormhole…
We show that there exist smooth, simply connected, four-dimensional spin manifolds which do not admit Einstein metrics, but nonetheless satisfy the strict Hitchin-Thorpe inequality. Our construction makes use of the Bauer/Furuta cohomotopy…
In this paper we will detail an approach to generate metrics and matter models on end-periodic manifolds, which are used extensively in the study of the exotic smooth structures of $\mathbb{R}^4$. We will present three distinct examples,…
In this paper we discuss the restrictions of the spacetime for the standard model of cosmology by using results of the differential topology of 3- and 4-manifolds. The smoothness of the cosmic evolution is the strongest restriction. The…
We explore local consequences of a non-zero cosmological constant on astrophysical structures. We find that the effects are not only sensitive to the density of the configurations but also to the geometry. For non-homogeneous…
From a purely geometric (kinematic) perspective, black holes in four dimensional spacetimes can have event horizons with arbitrary topologies. It is only when energy conditions are imposed that the horizon's topology is constrained to be…
There are investigated such cosmological models which instead of the usual spatial homogeneity property only fulfil the condition that in a certain synchronized system of reference all spacelike sections t = const. are homogeneous…
We use a variation of a classical construction of A. Hatcher to construct virtually all stable exotic smooth structures on compact smooth manifold bundles whose fibers have sufficiently large odd dimension (at least twice the base dimension…
Over the last two decades, many unexpected relations between exotic smoothness, e.g. exotic $\mathbb{R}^{4}$, and quantum field theory were found. Some of these relations are rooted in a relation to superstring theory and quantum gravity.…