Topological Equisingularity: Old Problems from a New Perspective (with an Appendix by G.-M. Greuel and G. Pfister on SINGULAR)

Javier Fernández de Bobadilla ()
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Javier Fernández de Bobadilla: IKERBASQUE, Basque Foundation for Science

Chapter Chapter 3 in Handbook of Geometry and Topology of Singularities III, 2022, pp 145-202 from Springer

Abstract: Abstract Among the various notions of equisingularity and equivalence of singularities, topological equisingularity is one of the oldest an easiest to define, 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 equisingularity, some of its relations with other equisingularity notions, and hint new possible approaches to old questions based in algebro-geometric methods, Floer theory and Lipschitz geometry. Topological equsingularity questions, were crucial motivation sources for the development of the Computer Algebra program SINGULAR; this is explained in an appendix by G.-M. Greuel and G. Pfister.

Date: 2022
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DOI: 10.1007/978-3-030-95760-5_3

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