Singularities ofJ-holomorphic curves in almost complex 4-manifolds

This note concerns the structure of singularities of mapsf from a neighborhood of {0} in the complex plane ? 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 S³ that depends only on the germC atx.