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<p>We extend the notion of topological T-duality from oriented sphere bundles to transgressive fibrations, a more general type fibration characterised by the abundance of transgressive elements. Examples of transgressive fibrations include principal <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\textrm{U}(n)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mtext>U</mtext> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-bundles therefore our notion of T-duality belongs to the realm of non-Abelian T-duality. We prove that transgressive T-duals have isomorphic twisted cohomology. We then introduce Clifford–Courant algebroids, show that one can assign such an algebroid to a transgressive fibration and that transgressive T-duals have isomorphic Clifford–Courant algebroids. We provide several examples illustrating different properties of T-dual spaces.</p>

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T-Duality for Transgressive Fibrations

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  • 发表日期：

    2025年10月3日

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  • Gil R. Cavalcanti

摘要

We extend the notion of topological T-duality from oriented sphere bundles to transgressive fibrations, a more general type fibration characterised by the abundance of transgressive elements. Examples of transgressive fibrations include principal \(\textrm{U}(n)\) U ( n ) -bundles therefore our notion of T-duality belongs to the realm of non-Abelian T-duality. We prove that transgressive T-duals have isomorphic twisted cohomology. We then introduce Clifford–Courant algebroids, show that one can assign such an algebroid to a transgressive fibration and that transgressive T-duals have isomorphic Clifford–Courant algebroids. We provide several examples illustrating different properties of T-dual spaces.