Topological T-duality for bundles of strongly self-absorbing C*-algebras and some physical applications

We extend the $C^{\ast }-$algebraic formalism of Topological T-duality to section algebras of locally trivial bundles of strongly self-absorbing $C^{\ast }-$algebras and to a larger class of String Theoretic dualities. We argue that physically this corresponds extending Topological T-duality to Flux Backgrounds of Type II String Theory which possess topologically nontrivial sourceless Ramond-Ramond flux. We demonstrate a map in $K-$theory for the $C^{\ast }-$algebras involved in both sides of this generalized duality. We calculate a few examples. We discuss the physical relevance of the above formalism in some detail, in particular, we argue that the above formalism models String Theoretic tree-level dualities found in such Flux Backgrounds such as Fermionic T-duality and Timelike T-duality.