Le Cycles and Hypersurface Singularities

This text describes and gives applications of an important new tool in the study of complex analytic hypersurface singularities: the Le cycles of the hypersurface. The Le cycles and their multiplicities - the Le numbers - provide effectively calculable data which generalizes the Milnor number of an isolated singularity to the case of singularities of arbitary dimension. The Le numbers control many topological and geometric properties of such non-isolated hypersurface singularities.