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THEORIES IN BRANE COSMOLOGY ARE TOPOLOGICALLY DUAL
Tozzi A., Peters JF
Our Universe could either lie on a spatial three-dimensional brane embedded in a higher dimensional bulk, or could be flanked by one or more multi-dimensional branes of different possible sizes and shapes. Here we demonstrate, based on novel topological findings, that disconnected strings with matching descriptions moving on a 4-brane (or more) project to a single string on a 3-brane. This means that strings travelling on the bulk or on higher dimensional branes necessarily display a counterpart in our 3D world, and vice versa. Furthermore, based on the concept of homotopy equivalence, we show how it is possible for branes to stitch together to become condensed branes. Our framework allows a topological duality among different brane theories, because it holds for all the types of branes, independent of their hypothetical shape, curvature, size and boundaries. Furthermore, a topological approach allow branes assessment in the general terms of particle trajectories taking place on donut-like manifolds. Indeed, every high-dimensional brane, independent on the subtending cosmological model, can be described in terms of multi-dimensional toruses mapping to branes with lower spatial dimensions.