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Fibrewise T-duality (Fourier-Mukai transform) for D-branes on an ellipticCalabi-Yau $X$ is shown to require naturally an appropriate twisting of theoperation respectively a twisted charge. The fibrewise T-duality is furthermoreexpressed through known monodromies in the context of Kontsevich'sinterpretation of mirror symmetry.Comment: 12 pages, harvma

Fibrewise T-duality for D-branes on elliptic Calabi-Yau