Analogues of Complex Geometry
Differential Geometry
2010-09-29 v6
Abstract
We prove that there are no pseudoholomorphic theories of anything other than curves, even if one allows more general spaces than almost complex manifolds. The proof is elementary, except for theories of pseudoholomorphic hypersurfaces, where topological techniques are needed. Surprisingly, hypersurface theories exist ``microlocally'' (in great abundance) to all orders perturbatively, but not ``locally.''
Cite
@article{arxiv.math/0107073,
title = {Analogues of Complex Geometry},
author = {Benjamin McKay},
journal= {arXiv preprint arXiv:math/0107073},
year = {2010}
}
Comments
33 pages, 0 figures, ver 2: theorems about hypersurface equations strengthened and typos corrected, ver 3: yet stronger results on hypersurface equations, ver 4: citations added, ver 5: more little insignificant errors fixed, ver 6: longer intro, reference to Kruglikov, a little more about hypersurface equations