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

In: Handbook of Geometry and Topology of Singularities III

Author

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  • Javier Fernández de Bobadilla

    (IKERBASQUE, Basque Foundation for Science
    BCAM, Basque Center for Applied Mathematics
    Academic Colaborator at UPV/EHU)

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.

Suggested Citation

  • Javier Fernández de Bobadilla, 2022. "Topological Equisingularity: Old Problems from a New Perspective (with an Appendix by G.-M. Greuel and G. Pfister on SINGULAR)," Springer Books, in: José Luis Cisneros-Molina & Lê Dũng Tráng & José Seade (ed.), Handbook of Geometry and Topology of Singularities III, chapter 0, pages 145-202, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-95760-5_3
    DOI: 10.1007/978-3-030-95760-5_3
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