Massey, David B. Singularities and enriched cycles. (English) Zbl 1068.32021 Pac. J. Math. 215, No. 1, 35-84 (2004). This paper is concerned with local topological and geometric properties of a complex analytic space with arbitrary singularities, that is to say, with the variety defined by a complex analytic function \(f\) on an open subset of \(\mathbb C^n\). A goal is to produce algebraic data that provide useful information about Thom’s \(a_f\) condition and the Milnor fibrations. To this end, the author introduces a new concept, namely graded, enriched characteristic cycles, in order to encode Morse modules of strata with respect to a constructible complex of sheaves. This generalizes previous results on perverse sheaves. Reviewer: Bruce Hughes (Nashville) Cited in 1 ReviewCited in 4 Documents MSC: 32S60 Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects) 32S30 Deformations of complex singularities; vanishing cycles 32S55 Milnor fibration; relations with knot theory Keywords:singular complex analytic space; Thom’s \(a_f\) condition; Milnor fibration; constructible sheaves; hypersurface; Whitney stratification PDFBibTeX XMLCite \textit{D. B. Massey}, Pac. J. Math. 215, No. 1, 35--84 (2004; Zbl 1068.32021) Full Text: DOI arXiv