Mathematical Research Letters

Volume 7, Issue 1, January 2000 pp. 35-53.

On the Unfolding of Folded Symplectic Structures

Authors: Ana Cannas da Silva, Victor Guillemin and Christopher Woodward
Author institution: University of California, Berkeley, Massachusetts Institute of Technology, and Rutgers University

Summary: 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.

Contents Full-Text PDF