Related papers: Curvature without connection
We investigate the possibility that a background independent quantum theory of gravity is not a theory of quantum geometry. We provide a way for global spacetime symmetries to emerge from a background independent theory without geometry. In…
Autoparallel curves along with geodesic curves can arise as trajectories of physical test bodies. We explicitly derive autoparallels as effective post-Riemannian geometric constructs, and at the same time we argue \emph{against} postulating…
We give a counterexample to a conjecture by Miasnikov, Ventura and Weil, stating that an extension of free groups is algebraic if and only if the corresponding morphism of their core graphs is onto, for every basis of the ambient group. In…
We formulate a mathematical theory of auxetic behavior based on one-parameter deformations of periodic frameworks. Our approach is purely geometric, relies on the evolution of the periodicity lattice and works in any dimension. We…
In terms of non-commutative geometry, we show that the $\sigma$--model can be built up by the gauge theory on discrete group $Z_2$. We introduce a constraint in the gauge theory, which lead to the constraint imposed on linear $\sigma$ model…
The theory of Lie systems has recently been applied to Quantum Mechanics and additionally some integrability conditions for Lie systems of differential equations have also recently been analysed from a geometric perspective. In this paper…
We describe simply connected compact exceptional simple Lie groups in very elementary way. We first construct all simply connected compact exceptional Lie groups G concretely. Next, we find all involutive automorphisms of G, and determine…
We examine the heap of linear connections on anchored vector bundles and Lie algebroids. Naturally, this covers the example of affine connections on a manifold. We present some new interpretations of classical results via this ternary…
We show that the general method of Lie algebra expansions can be applied to re-construct several algebras and related actions for non-relativistic gravity that have occurred in the recent literature. We explain the method and illustrate its…
In the paper two important theorems about complete affine spheres are generalized to the case of statistical structures on abstract manifolds. The assumption about constant sectional curvature is replaced by the assumption that the…
Examples of nonformal simply connected symplectic manifolds are constructed.
Using the notion of existentially closed structures, we obtain embedding theorems for groups and Lie algebras. We also prove the existence of some groups and Lie algebras with prescribed properties.
Tangle-tree theorems are an important tool in structural graph theory, and abstract separation systems are a very general setting in which tangle-tree theorems can still be formulated and proven. For infinite abstract separation systems, so…
A theory of principal bundles possessing quantum structure groups and classical base manifolds is presented. Structural analysis of such quantum principal bundles is performed. A differential calculus is constructed, combining differential…
This paper is the third in a series dedicated to the fundamentals of sub-Riemannian geometry and its implications in Lie groups theory: "Sub-Riemannian geometry and Lie groups. Part I", math.MG/0210189, available at…
New expansionary and rotational quadratic forms are constructed for $E^n$-endomorphisms. Relations amongst the various eigenvalues, eigendirections and matrix invariants are established, including propositions on complexity and geometric…
We adapt the classical notion of learning from text to computable structure theory. Our main result is a model-theoretic characterization of the learnability from text for classes of structures. We show that a family of structures is…
We introduce a geometric construction of a gauge field theory of a complex adaptive system. It is based on a suitable simplicial formulation of a discrete geometry that manifests relevant properties valid in the classical differentiable…
The new approach to quantize the gravity based on the notion of differential algebra is suggested. It is shown that the differential geometry of this object can not be described in terms of points. The spatialization procedure giving rise…
This paper develops some of the methods of the "Italian School" of algebraic geometry in the context of infinitesimals. The results of this paper have no claim to originality, they can be found in Severi, we have only made the arguments…