An example is given which shows that the Denef–Loeser zeta function (usually called the topological
zeta function) associated to a germ of a complex hypersurface singularity is not a topological invariant
of the singularity. The idea is the following. Consider two germs of plane curves singularities with the
same integral Seifert form but with different topological type and which have different topological zeta
functions. Make a double suspension of these singularities (consider them in a 4-dimensional complex
space). A theorem of M. Kervaire and J. Levine states that the topological type of these new hypersurface
singularities is characterized by their integral Seifert form. Moreover the Seifert form of a suspension is
equal (up to sign) to the original Seifert form. Hence these new singularities have the same topological
type. By means of a double suspension formula the Denef–Loeser zeta functions are computed for the
two 3-dimensional singularities and it is verified that they are not equal.