Pseudoholomorphic maps into folded symplectic four-manifolds

@inproceedings{Bergmann2008PseudoholomorphicMI,
title={Pseudoholomorphic maps into folded symplectic four-manifolds},
author={Jens von Bergmann and Cannas da Silva and Victor Guillemin},
year={2008}
}

Every oriented 4–manifold admits a stable folded symplectic structure, which in turn determines a homotopy class of compatible almost complex structures that are discontinuous across the folding hypersurface (“fold”) in a controlled fashion. We define folded holomorphic maps, ie pseudoholomorphic maps that are discontinuous across the fold. The boundary values on the fold are mediated by tunneling maps which are punctured H–holomorphic maps into the folding hypersurface with prescribed… CONTINUE READING