A theory of gravity with torsion is examined in which the torsion tensor is constructed from the exterior derivative of an antisymmetric rank two potential plus the dual of the gradient of a scalar field. Field equations for the theory are derived by demanding that the action be stationary under variations with respect to the metric, the antisymmetric potential, and the scalar field. A material...

We compute the equivariant K-homology of the classifying space for proper actions, for cocompact 3-dimensional hyperbolic reflection groups. This coincides with the topological K-theory of the reduced C∗-algebra associated to the group, via the Baum-Connes conjecture. We show that, for any such reflection group, the associated K-theory groups are torsion-free. This means that we can complete pr...

This paper studies the self-dual Einstein-Dirac theory. A generalization is obtained of the Jacobson-Smolin proof of the equivalence between the self-dual and Palatini purely gravitational actions. Hence one proves equivalence of self-dual EinsteinDirac theory to the Einstein-Cartan-Sciama-Kibble-Dirac theory. The Bianchi symmetry of the curvature, core of the proof, now contains a non-vanishin...

We study D1-branes on the fourfold C/(Z2 × Z2 × Z2), in the presence of discrete torsion. Discrete torsion is incorporated in the gauge theory of the D1-branes by considering a projective representation of the finite group Z2 × Z2 × Z2. The corresponding orbifold is then deformed by perturbing the F-flatness condition of the gauge theory. The moduli space of the resulting gauge theory retains a...

We establish certain ‘homological properties’ of the stable Higson corona used by Emerson and Meyer to study the Dirac-dual-Dirac approach to the Baum-Connes conjecture [5]. These are used to obtain explicit isomorphisms between the K-theory of the stable Higson corona of certain spaces X and the topological K-theory of natural geometric boundaries of X. This is sufficient to give a simple proo...

In this paper we analyze discrete torsion in perturbative heterotic string theory. In previous work we have given a purely mathematical explanation of discrete torsion as the choice of orbifold group action on a B field, in the case that dH = 0; in this paper we perform the analogous calculations in heterotic strings where dH = 0.

KT-geometry is the geometry of a Hermitian connection whose torsion is a 3-form. HKT-geometry is the geometry of a hyper-Hermitian connection whose torsion is a 3-form. We identify non-trivial conditions for a reduction theory for these types of geometry.

We prove that every perfect torsion theory for a ring R is differential (in the sense of [2]). In this case, we construct the extension of a derivation of a right R-module M to a derivation of the module of quotients of M . Then, we prove that the Lambek and Goldie torsion theories for any R are differential.

We make it precise what it means to have a connection with torsion as solution of the Einstein equations. While locally the theory remains the same, the new formulation allows for topologies that would have been excluded in the standard formulation of gravity. In this formulation it is possible to couple arbitrary torsion to gauge fields without breaking the gauge invariance.

We study the effect of mass on geometric descriptions of gauge field theories. In an approach in which the massless theory resembles general relativity, the introduction of the mass entails non-zero torsion and the generalization to Einstein-Cartan-Sciama-Kibble theories. The relationships to pure torsion formulations (teleparallel gravity) and to higher gauge theories are also discussed.