A derived-geometric definition of p-form connections on infinity-bundles is given via splittings of the Atiyah L-infinity-algebroid, recovering Cech-Deligne cocycles for higher U(1)-bundles.
Generalized Calabi-Yau manifolds
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abstract
A geometrical structure on even-dimensional manifolds is defined which generalizes the notion of a Calabi-Yau manifold and also a symplectic manifold. Such structures are of either odd or even type and can be transformed by the action of both diffeomorphisms and closed 2-forms. In the special case of six dimensions we characterize them as critical points of a natural variational problem on closed forms, and prove that a local moduli space is provided by an open set in either the odd or even cohomology.
years
2026 2verdicts
UNVERDICTED 2representative citing papers
Courant algebroid relations define spinor and Dirac structure relations, with T-duality inducing spinor relations that generalize twisted cohomology isomorphisms and are compatible with Type II supergravity equations.
citing papers explorer
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Symmetries and Higher-Form Connections in Derived Differential Geometry
A derived-geometric definition of p-form connections on infinity-bundles is given via splittings of the Atiyah L-infinity-algebroid, recovering Cech-Deligne cocycles for higher U(1)-bundles.
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Generalised Complex and Spinor Relations
Courant algebroid relations define spinor and Dirac structure relations, with T-duality inducing spinor relations that generalize twisted cohomology isomorphisms and are compatible with Type II supergravity equations.