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Journal of the London Mathematical Society Advance Access originally published online on July 31, 2007
Journal of the London Mathematical Society 2007 76(1):16-40; doi:10.1112/jlms/jdm037
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© 2007 London Mathematical Society

Analogues of complex geometry

Benjamin McKay

School of Mathematics
University College Cork
Cork
Ireland

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’.

b.mckay{at}ucc.ie

2000 Mathematics Subject Classification 53D99, 35F20.

Received August 22, 2005; revised May 17, 2006; published online July 31, 2007.


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