Mathematical Research Letters

Volume 7 (2000)

Number 1

On the Unfolding of Folded Symplectic Structures

Pages: 35 – 53



Victor Guillemin (Massachusetts Institute of Technology)

Ana Cannas da Silva (University of California at Berkeley)

Christopher Woodward (Rutgers University)


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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