Singularities of mappings and the vanishing homology of images and discriminants. (English) Zbl 1372.32002

Mond, David

Araújo dos Santos, Raimundo Nonato (ed.) et al., School on real and complex singularities in São Carlos, Brazil, July 16–21, 2012 and 12th international workshop on real and complex singularities, São Carlos, Brazil, July 22–27, 2012. Lecture notes. Tokyo: Mathematical Society of Japan (MSJ) (ISBN 978-4-86497-030-3/hbk). Advanced Studies in Pure Mathematics 68, 41-142 (2016).

Summary: These notes provide an introduction to the theory of singularities of mappings and right-left equivalence. They cover a part of Mather theory, concerned with stability, classification and deformations, and go on to study the vanishing homology of images and discriminants of families of mappings. A number of open questions are discussed in the last three sections.
For the entire collection see [Zbl 1353.00009].

MSC:

32-02	Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces
14-02	Research exposition (monographs, survey articles) pertaining to algebraic geometry
32S05	Local complex singularities
32S30	Deformations of complex singularities; vanishing cycles
14B05	Singularities in algebraic geometry
14P25	Topology of real algebraic varieties

Keywords:

singularities of mappings; equivalence of germs of mappings