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, U ∩C) is homeomorphic to the cone overS^{3},K_{x} whereK_{x} is an algebraic knot in S^{3} that depends only on the germC atx.

Math Subject Classification

53C15

Key Words and Phrases

Almost complex manifoldholomorphic curvesingularitysymplectic geometry