We introduce topological T-duality (Bunke/Schick) and C*-algebraic T- duality (Mathai/Rosenberg) and explain how they are connected. A future task is to find a symmetric duality for non-commutative tori generalising the work of Mathai/Rosenberg.
Links:
[1] https://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/node/3444
[3] https://www.mpim-bonn.mpg.de/node/249