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Analogues of complex geometry
Author(s) -
McKay Benjamin
Publication year - 2007
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdm037
Subject(s) - hypersurface , mathematics , pure mathematics , link (geometry) , geometry , topology (electrical circuits) , combinatorics
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’.