We study the causality relation in the 3-dimensional anti-de Sitter space AdS and its conformal boundary $\mathrm{Ein}_2$. To any closed achronal subset $\Lambda$ in $\mathrm{Ein}_2$ we associate the invisible domain $E(\Lambda)$ from $\Lambda$ in AdS. We show that if $\Gamma$ is a torsion-free discrete group of isometries of AdS preserving $\Lambda$ and is non-elementary (for example, not abelian) then the action of $\Gamma$ on $E(\Lambda)$ is free, properly discontinuous and strongly causal. If $\Lambda$ is a topological circle then the quotient space $M_\Lambda(\Gamma) = \Gamma\setminus E(\Lambda)$ is a maximal globally hyperbolic AdS-spacetime admitting a Cauchy surface $S$ such that the induced metric on $S$ is complete. In a forthcoming paper we study the case where $\Gamma$ is elementary and use the results of the present paper to define a large family of AdS-spacetimes including all the previously known examples of BTZ multi-black holes.

We discuss the resolution of toroidal orbifolds. For the resulting smooth Calabi–Yau manifolds, we calculate the intersection ring and determine the divisor topologies. In a next step, the orientifold quotients are constructed..

We study topological T-duality for spaces with a semi-free $S^{1}$-action with isolated fixed points. Physically, these correspond to spacetimes containing Kaluza–Klein monopoles. We demonstrate that the physical dyonic coordinate of such spaces has an analogue in our formalism. By analogy with the Dirac monopole, we study these spaces as gerbes. We study the effect of topological T-duality on these gerbes.