The link of suspension singularities and Zariski's conjecture
This thesis is devoted to singularity theory. It is shown that some families of isolated hypersurface singularities have special and surprising properties. More precisely, we consider suspension hypersurface singularities of type g = f (x, y) + z n, where f is an irreducible plane curve singularity. For such germs, we prove that the link of g determines completely the Newton pairs of f and the integer n except for two pathological cases, which can be completely described. Even in the pathological cases, the link and the Milnor number of g determine uniquely the Newton pairs of f and n. One of the consequences of the result is that one recovers the equisingular type of [g = 0] from its topology, in particular, (almost) all the analytic invariants of g. For such g , as a consequence, we obtain Zariski's conjecture about the multiplicity. We also verify these results for a weighted homogeneous singularity whose link is a rational homology sphere.