Interaction de Strates Consécutives II

Abstract

This article completes the results of our previous paper [B.91] on interaction of consecutive strata for the vanishing cycles. In the same context that loc. cit., we treat here the tangling phenomenon for a given cohomology class of the Milnor’s fiber of $f$ at the origin in the case where its nilpotency order for the given eigenvalue $e^{-2_i\pi .u}\ne 1$ of the monodromy is not necessarily bigger or equal than the nilpotency order of the monodromy for this eigenvalue at the generic point of the big stratum. We show that this tangling phenomenon can always be detected on the poles of the meromorphic extension of the distribution ${\int }_X|f{|}^{2\lambda }\square$.