Dual curves and pseudoholomorphic curves

Details Dual curves and pseudoholomorphic curves Dual curves and pseudoholomorphic curves

2001-01-02

arxiv.org/abs/math/0101017v3

Selecta Mathematica N.S., 9 (2003), pp. 251-311

Mathematics

Differential Geometry

50 pages. LaTeX 2e, to appear in Selecta Mathematica, v2: typos, v3: small points clarified for referees' satisfaction; see

Scientific paper

A notion of dual curve for pseudoholomorphic curves in 4--manifolds turns out to be possible only if the notion of almost complex structure structure is slightly generalized. The resulting structure is as easy (perhaps easier) to work with, and yields many analogues of results in complex surface theory, using a description of the local geometry via Cartan's method of equivalence. Duality then uncovers a new infinite-dimensional family of geometric integrable systems. These are the first steps toward geometry on moduli spaces of pseudoholomorphic curves.

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