Dual curves and pseudoholomorphic curves

• Benjamin McKay ^[1]
  1. [1] University of Utah

     University of Utah

     Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 9, Nº. 2, 2003, págs. 251-311
• Idioma: inglés
• DOI: 10.1007/s00029-003-0304-z
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• Resumen

  • 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.