Titlebook: Handbook of Geometry and Topology of Singularities III; José Luis Cisneros-Molina,Lê Dũng Tráng,José Seade Book 2022 Springer Nature Switz

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Book 2022mplex analytic varieties, nearby and vanishing cycles, and more...Singularities are ubiquitous in mathematics and science in general. Singularity theory interacts energetically with the rest of mathematics, acting as a crucible where different types of mathematical problems interact, surprising conn

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Singularities of Mappings,ain how to calculate some of the key invariants: the .-codimension, the determinacy degree, and a minimal versal unfolding, introducing a new technique which lead to easily implementable computer algorithms. We then describe the topology of stable perturbations of .-finite germs, and in particular t

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Topological Equisingularity: Old Problems from a New Perspective (with an Appendix by G.-M. Greuel but it is far to be well understood and several challenging questions remain open. Important examples are Zariski multiplicity conjecture and the charaterization of topological triviality of families of isolated and non-isolated singularities. In this chapter we survey developments in topological eq

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Residues and Hyperfunctions,e residues that arise from the localization of characteristic classes via the Alexander duality. The relative Čech-de Rham theorem allows us to deal with the problem from both the topological and differential geometric viewpoints and the comparison of the two yields various interesting expressions o