Singularities of Mappings

David Mond received his PhD at the University of Liverpool and has held positions at the National University of Colombia, Bogotá, and at the University of Warwick, where he is a full professor. His main field of research is the theory of singularities of mappings, especially the geometry and topology of images and discriminants, and their relation to the deformation theory of unstable germs map-germs.Juan J. Nuño-Ballesteros is Professor at the University of Valencia. His research is in the field of singularities of real and complex mappings and his main contributions to the subject include the topological classification of real analytic map-germs and also the Whitney equisingularity of complex analytic families of map-germs. He has also other important contributions in generic geometry (applications of Singularity Theory to the differential geometry of submanifolds in Euclidean spaces) and about global aspects of singularities of smooth mappings.

“Exercises at the end of each section are intended to help the interested reader to study the material in depth. … In general, this book is a nice supplement to the classical and modern monographs devoted to various sides of singularity theory. It comprises a lot of material scattered throughout numerous papers and presents it in a systematic and rigorous way. No doubt, it will become a common reference for various issues covered in this book.” (Eugenii Shustin, Mathematical Reviews, January, 2023)“The book is written in a clear pedagogical style; it contains many examples, exercises, comments, remarks, nice pictures, very useful instructive and systematic references, computational algorithms with implementation in the computer algebra software systems Macaulay 2 and Mathematica, etc. … Without a doubt, the book is understandable, interesting and useful for graduate students and can serve as a good starting point for those who are interested in various aspects of both pure and applied mathematics.” (Aleksandr G. Aleksandrov, zbMATH 1448.58032, 2020)

• Introduction.- Part I Thom-Mather Theory: Right-Left Equivalence, Stability,Versal Unfoldings, Finite Determinacy.- Manifolds and Smooth Mappings.- Left-Right Equivalence and Stability.- Contact Equivalence.- Versal Unfoldings.- Finite Determinacy.- Classification of Stable Germs by Their Local Algebras.- Part II Images and Discriminants: The Topology of Stable Perturbations.- Stable Images and Discriminants.- Multiple Points.- Calculating the Homology of the Image.- Multiple Points in the Target: The Case of Parameterised Hypersurfaces.- Appendix A: Jet Spaces and Jet Bundles.- Appendix B Stratifications.- Appendix C Background in Commutative Algebra.- Appendix D Local Analytic Geometry.- Appendix E Sheaves. References.- Index