Analogues of Complex Geometry

Details Analogues of Complex Geometry Analogues of Complex Geometry

2001-07-10

arxiv.org/abs/math/0107073v6

J. Lond. Math. Soc. (2) 76 (2007), no. 1, 16--40

Mathematics

Differential Geometry

33 pages, 0 figures, ver 2: theorems about hypersurface equations strengthened and typos corrected, ver 3: yet stronger result

Scientific paper

10.1112/jlms/jdm037

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.''

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