Numerical Control over Complex Analytic Singularities

Overview Part I. Algebraic Preliminaries: Gap Sheaves and Vogel Cycles: Introduction Gap sheaves Gap cycles and Vogel cycles The Le-Iomdine-Vogel formulas Summary of Part I Part II. Le Cycles and Hypersurface Singularities: Introduction Definitions and basic properties Elementary examples A handle decomposition of the Milnor fibre Generalized Le-Iomdine formulas Le numbers and hyperplane arrangements Thom's $a_f$ condition Aligned singularities Suspending singularities Constancy of the Milnor fibrations Another characterization of the Le cycles Part III. Isolated Critical Points of Functions on Singular Spaces: Introduction Critical avatars The relative polar curve The link between the algebraic and topological points of view The special case of perverse sheaves Thom's $a_f$ condition Continuous families of constructible complexes Part IV. Non-Isolated Critical Points of Functions on Singular Spaces: Introduction Le-Vogel cycles Le-Iomdine formulas and Thom's condition Le-Vogel cycles and the Euler characteristic Appendix A. Analytic cycles and intersections Appendix B. The derived category Appendix C. Privileged neighborhoods and lifting Milnor fibrations References Index