Stratified Picard-Lefschetz Theory with Twisted Coefficients
  The monodromy action in the homology (generally with twisted coefficients) of complements of stratified complex analytic varieties depending on parameters is studied. For a wide class of local degenerations of such families (stratified Morse singularities) local monodromy and variation operators are reduced to similar operators acting in the transversal slices of corresponding strata. In particular, these results imply a main part of F. Pham's generalized Picard--Lefschetz formulae. 
Victor A. Vassiliev
math.AG