Malte Arthur Kunath

• From a physicists point of view T-duality is a relation connecting string theories on different spacetimes. Mathematically speaking, T-duality should be a symmetric relation on the space of toroidal string backgrounds. Such a background consists of: a smooth manifold M; a torus bundle E over M - the total space modelling spacetime; a Riemannian metric g on E - modelling the field of gravity; a U(1)-bundle gerbe G with connection over E - modelling the Kalb- Ramond field. But as of now no complete model for T-duality exists. The three most notable approaches for T-duality are given by the differential approaches by Buscher in the form of the Buscher rules and by Bouwknegt, Evslin and Mathai in the form of T-duality with H-flux on the one hand, and by the topological approach given by Bunke, Rumpf and Schick which is known as topological T-duality. In this thesis we combine these different approaches to form the first model for T-duality over complete geometric toroidal string backgrounds and we will introduce an example for this geometric T-duality inspired by the Hopf bundle.