Topological Spherical T-duality -- Dimension change from higher degree H-flux

Topological Spherical T-duality was introduced by Bouwknegt, Evslin and Mathai in [BEM15] as an extension of topological T-duality from S¹ bundles to SU(2)-bundles endowed with closed 7-forms. This notion was further extended to sphere bundles by Lind, Sati and Westerland [LSW16] as a duality between S²ⁿ⁻¹-bundles endowed with closed $(4n-1)$-forms. We generalise this relation one step further and define T-duality for S²ⁿ⁻¹-bundles endowed with closed odd forms of arbitrary degree. The degree of the form determines the dimension of the fibers of the dual spaces. We show that T-duals exist and, as in the previous cases, T-dual spaces have isomorphic twisted cohomology.