Relative Polar Multiplicities and the Real Link

Abstract

For a hypersurface defined by a complex analytic function, we obtain a chain complex of free abelian groups, with ranks given in terms of relative polar multiplicities, which has cohomology isomorphic to the reduced cohomology of the real link. This leads to Morse-type inequalities between the Betti numbers of the real link of the hypersurface and the relative polar multiplicities of the function.