New gluing framework produces torsion-free Spin(7)-manifolds resolving compact Spin(7)-orbifolds, with the gluing obstruction shown equivalent to matching Chen-Ruan cohomology in the codimension-four case.
Deformations of calibrations, {Calabi-Yau, HyperK\"ahler, $G_2$ and Spin(7) structures}
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abstract
We shall develop a new deformation theory of geometric structures in terms of closed differential forms. This theory is a generalization of Kodaira -Spencer theory and further we obtain a criterion of unobstructed deformations. We apply this theory to certain geometric structures: Calabi-Yau, HyperK\"ahler, $\G$ and $\Spin$ structures and show that these deformation spaces are smooth in a systematic way.
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math.DG 1years
2025 1verdicts
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Spin(7)-Orbifold Resolutions
New gluing framework produces torsion-free Spin(7)-manifolds resolving compact Spin(7)-orbifolds, with the gluing obstruction shown equivalent to matching Chen-Ruan cohomology in the codimension-four case.