On the unfolding of folded symplectic structures

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Abstract

A folded symplectic structure is a closed 2-form which is nondegenerate except on a hypersurface, and whose restriction to that hypersurface has maximal rank. We show how a compact manifold equipped with a folded symplectic structure can sometimes be broken apart, or "unfolded", into honest compact symplectic orbifolds. A folded symplectic structure induces a spin-c structure which is canonical (up to homotopy). We describe how the index of the spin-c Dirac operator behaves with respect to unfolding.

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Cannas Da Silva, A., Guillemin, V., & Woodward, C. (2000). On the unfolding of folded symplectic structures. Mathematical Research Letters, 7(1), 35–53. https://doi.org/10.4310/mrl.2000.v7.n1.a4

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