Topological T-Duality for Twisted Tori

We apply the $C^*$-algebraic formalism of topological T-duality due to Mathai and Rosenberg a broad class spaces that include torus bundles appearing in string theory compactifications with duality twists, such as nilmanifolds, well many other examples. develop simple procedure this setting for constructing T-duals starting from commutative $C^*$-algebra an action ${\mathbb R}^n$. treat general almost abelian solvmanifolds arbitrary dimension detail, where we provide necessary sufficient criteria existence classical terms purely group theoretic data, compute them explicitly continuous-trace algebras non-trivial Dixmier-Douady classes. prove any solvmanifold has T-dual given by bundle noncommutative tori, which also explicitly. The monodromy original becomes Morita equivalence among fiber algebras, so these $C^*$-algebras rigorously describe T-folds non-geometric theory.