  By analyzing super-torsion and brane super-cocycles, we derive a new duality
in M-theory, which takes the form of a higher version of T-duality in string
theory. This involves a new topology change mechanism abelianizing the 3-sphere
associated with the C-field topology to the 517-torus associated with
exceptional-generalized super-geometry. Finally we explain parity symmetry in
M-theory within exceptional-generalized super-spacetime at the same level of
spherical T-duality, namely as an isomorphism on 7-twisted cohomology.
