The Journal of Geometric Analysis

, Volume 2, Issue 3, pp 249–266

Singularities ofJ-holomorphic curves in almost complex 4-manifolds

  • Dusa McDuff

DOI: 10.1007/BF02921295

Cite this article as:
McDuff, D. J Geom Anal (1992) 2: 249. doi:10.1007/BF02921295


This note concerns the structure of singularities of mapsf from a neighborhood of {0} in the complex plane ℂ to an almost complex manifold (V, J), which areJ-holomorphic in the sense thatdf oi =J odf and are singular (i.e.,df = 0) at {0}. The main result is that whenV has dimension 4, the topology of these singularities is the same as in the case whenJ is integrable. Thus, if the image Imf =C is not multiply-covered, there is a neighborhoodU of the pointx = f(0), such that the pair (U, UC) is homeomorphic to the cone overS3,Kx whereKx is an algebraic knot in S3 that depends only on the germC atx.

Math Subject Classification


Key Words and Phrases

Almost complex manifoldholomorphic curvesingularitysymplectic geometry

Copyright information

© CRC Press, Inc 1992

Authors and Affiliations

  • Dusa McDuff
    • 1
  1. 1.Department of MathematicsSUNY at Stony BrookStony BrookUSA