Related papers: On 4-dimensional Lorentz-structures, Dark energy a…
We discuss the influence of dark energy on structure formation, especially the effects on \sigma_8. Our interest is particularly focused on quintessence models with time-dependent equation of state and non-negligible quintessence component…
In this paper, we investigate existence of inequivalent smooth structures on closed smooth non-orientable 4-manifolds building upon results of Akbulut, Cappell-Shaneson, Fintushel-Stern, Gompf, and Stolz. We add to the number of known…
In connection with recent discussion of topological order and topological phase transitions in quantum systems, we reexamine circumstances that lead to the appearance of a topological glass in certain classical lattice spin models. Local…
We investigate the uniqueness of so-called exotic structures on certain exact symplectic manifolds by looking at how their symplectic properties change under small nonexact deformations of the symplectic form. This allows us to distinguish…
Four-dimensional spacetime, together with a natural generalisation to extra dimensions, is obtained through an analysis of the structures and symmetries deriving from possible arithmetic expressions for one-dimensional time. On taking the…
We investigate the dynamics of the geometric transitions associated to compactified spacetimes. By including the dynamics of gravity we are able to follow the evolution of collapsing cycles as they attempt to undergo a topology changing…
In this letter we show that in a Kaluza-Klein framework we can have arbitrary topology change between the macroscopic (i.e. noncompactified) spacelike 3-hypersurfaces. This is achieved by using the compactified dimensions as a catalyser for…
We investigate topology changing processes in the WKB approximation of four dimensional quantum cosmology with a negative cosmological constant. As Riemannian manifolds which describe quantum tunnelings of spacetime we consider constant…
This paper studies properly embedded surfaces in the 4-ball that are exotically knotted (i.e., topologically but not smoothly isotopic), and leverages this local phenomenon to study surfaces in larger 4-manifolds. The main results provide a…
The fact that the energy densities of dark energy and matter are similar currently, known as the coincidence problem, is one of the main unsolved problems of cosmology. We present here a model in which a spatial curvature of the universe…
Motivated by condensed matter physical systems, in which a finite-time singularity indicates that the topology of the system changes, we critically examine the possibility of the Universe's topology change at a finite-time cosmological…
This paper studies the situation when two 4-dimensional Lorentz manifolds (that is, space-times) admit the same (unparametrised) geodesics, that is, when they are projectively related. A review of some known results is given and then the…
We show that many explicit examples of exotic pairs of surfaces in a smooth 4-manifold become smoothly isotopic after one external stabilization with $S^2\times S^2$ or $CP^2\#\overline{CP^2}$. Our results cover surfaces produced by…
We construct a rational homotopy-theoretic model for a classifying space of locally conformally symplectic structures on four-manifolds, and use it to definition a cobordism category of three-manifolds `anchored' by principal $\Omega^2 S^2$…
We study topological properties of automorphisms of 4-dimensional torus generated by integer symplectic matrices. The main classifying element is the structure of the topology of a foliation generated by unstable leaves of the automorphism.…
Theories of low-energy Lorentz violation by a fixed-norm "aether" vector field with two-derivative kinetic terms have a globally bounded Hamiltonian and are perturbatively stable only if the vector is timelike and the kinetic term in the…
This survey reviews recent advances connecting link homology theories to invariants of smooth 4-manifolds and extended topological quantum field theories. Starting from joint work with Morrison and Walker, I explain how functorial link…
Dark energy might have an influence on the formation of non--linear structures during the cosmic history. For example, in models in which dark energy couples to dark matter, it will be non--homogeneous and will influence the collapse of a…
We follow the point of view that superstring theory, as the theory of quantum gravity in the number of spacetime dimensions bigger than 4, serves as mathematics for both, 4 dimensional QG and exotic smoothness on open 4-manifolds.…
We analyze the global theory of boundary conditions for a constrained quantum system with classical configuration space a compact Riemannian manifold $M$ with regular boundary $\Gamma=\partial M$. The space $\CM$ of self-adjoint extensions…