Related papers: Exotic smoothness and particle physics
Peculiar properties of many classical and quantum systems can be related to, or derived from those of a free particle. In this way we explain the appearance and peculiarities of the exotic nonlinear Poincar\'e supersymmetry in…
Random invariant manifolds are geometric objects useful for understanding complex dynamics under stochastic influences. Under a nonuniform hyperbolicity or a nonuniform exponential dichotomy condition, the existence of random pseudo-stable…
This thesis discusses exotic 7-spheres, i.e. manifolds that are homeomorphic but not diffeomorphic to the ordinary 7-sphere, using a set of analytical and computational tools from theoretical physics. The theory of fibre bundles and…
Simplicial, piecewise-flat discretizations of manifolds provide a clear path towards curvature analysis on discrete geometries and for solutions of PDE's on manifolds of complex topologies. In this manuscript we review and expand on…
We construct an infinite family of mutually non-diffeomorphic irreducible smooth structures on the topological 4-manifold $S^2 \times S^2$.
Normally one assumes isolated surface singularities to be normal. The purpose of this paper is to show that it can be useful to look at nonnormal singularities. By deforming them interesting normal singularities can be constructed, such as…
We extend to manifolds endowed with a general geometric structure, the classical notions of gradient as well as Laplace operator, and provide some of their natural properties.
Exterior calculus and moving frames are used to describe curved elastic shells. The kinematics follow from the Lie-derivative on forms whereas the dynamics via stress-forms.
We study the relationship between exotic R^4's and Stein surfaces as it applies to smoothing theory on more general open 4-manifolds. In particular, we construct the first known examples of large exotic R^4's that embed in Stein surfaces.…
The nature of cosmological dark matter finds its explanation in physics beyond the Standard model of elementary particles. The landscape of dark matter candidates contains a wide variety of species, either elusive or hardly detectable in…
We give an elementary introduction to hyperk\"ahler manifolds, survey some of their interesting properties and some open problems.
Exotic sheaves are certain complexes of coherent sheaves on the cotangent bundle of the flag variety of a reductive group. They are closely related to perverse-coherent sheaves on the nilpotent cone. This expository article includes the…
We sharpen a recent observation by Tim Maudlin: differential calculus is a natural language for physics only if additional structure, like the definition of a Hodge dual or a metric, is given; but the discrete version of this calculus…
These notes are designed for those who either plan to work in differential geometry, or at least want to have a good reason not to do it. We discuss smooth curves and surfaces -- the main gate to differential geometry. We focus on the…
We explore different (and complementary) views of spinors and their exotic counterparts, linking the very existence of the later to the presence of black holes. Moreover, we investigate the effects of the exotic term in the Hawking…
In years to come, we shall see substantial progress in our understanding of nuclear structure - a rich and many-faceted field. An important element in this task will be to extend the study of nuclei into new domains. The journey to 'the…
Deformational structures, in many aspects generalizing standard elasticity theory, are investigated in abstract form. Within free deformational structures we define algebra of deformations, classify them by its special properties, define…
A pedagogical overview of strange quark matter and strange stars is presented. After a historical notation of the research and an introduction to quark matter, a major part is devoted to the physics and astrophysics of strange stars, with…
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.…
A number of topics involving metrics and measures are discussed, including some of the special structure associated with ultrametrics.