Related papers: A note on commutative and noncommutative Gurariy s…

Following the general principles of noncommutative geometry, it is possible to define a metric on the space of pure states of the noncommutative algebra generated by the coordinates. This metric generalizes the usual Riemannian one. We…

We give a dual to the McKay correspondence, involving conjugacy classes of subgroups of SU(2). We prove a determinantal formula involving both correspondences. We pose some questions concerning a non-commutative Fourier transform.

The validity of non-perturbative methods is questioned. The concept of relative space is introduced.

We develop a $GL_{qp}(2)$ invariant differential calculus on a two-dimensional noncommutative quantum space. Here the co-ordinate space for the exterior quantum plane is spanned by the differentials that are commutative (bosonic) in nature.

The purpose of these survey notes is to give a presentation of a classical theorem of Nomizu that relates the invariant affine connections on reductive homogeneous spaces and nonassociative algebras.

We use the compression theorem (arxiv:math.GT/9712235) cf section 7, to prove results for equivariant configuration spaces analogous to the well-known non-equivariant results of May, Milgram and Segal.

We derive general conditions under which geodesics of stationary spacetimes resemble trajectories of charged particles in an electromagnetic field. For large curvatures (analogous to strong magnetic fields), the quantum mechanicical states…

Among the many worthwhile quantum experiments taking advantage of long baselines in space, this white paper points to the far-reaching significance of gravitational decoherence experiments. These experiments can provide clues as to whether…

The aim of this paper is to clarify the properties of semi-barrelled spaces (also called countably quasi-barrelled spaces in the literature). These spaces were studied by several authors, in particular in the classical book of N. Bourbaki…

In this note we introduce a new family of non-commutative spaces that we call non-commutative toric varieties and we describe some of their main properties. The main technical tool in this investigation is a natural extension of LVM-theory…

These notes give an elementary approach to parts of the theory of standard Borel and analytic spaces.

We review some applications of noncommutative geometry to the study of transverse geometry of Riemannian foliations and discuss open problems.

We investigate a conformal-like transformation for which the spacetime interval is invariant.

In this paper we show that in the case of noncommutative two-tori one gets in a natural way simple structures which have analogous formal properties as Hopf algebra structures but with a deformed multiplication on the tensor product.

After reviewing Gribov ambiguity of non-Abelian gauge theories, a phenomenon related to the topology of the bundle of gauge connections, we show that there is a similar feature for noncommutative QED over Moyal space, despite the structure…

This paper is the second in a series exploring the properties of a functor which assigns a homotopy double groupoid with connections to a Hausdorff space. We show that this functor satisfies a version of the van Kampen theorem, and so is a…

The symmetries of Unimodular Gravity are clarified somewhat.

We make some remarks on the existence of a geodesically complete core for any compact non-positively curved space.

We investigate gravitational radiation in dynamical noncommutative spaces. By including corrections to the gravitational potential due to dynamical noncommutativity, we calculate the power in gravitational radiation and use observational…

We prove a Galois correspondence theorem for groupoids acting orthogonally and partially on commutative rings. We also consider partial actions that are not orthogonal, presenting two correspondences in this case: one for strongly Galois…