V.I. Arnold Singularities of Differentiable Maps Volume I

This book, "Singularities of Differentiable Maps", is Volume I of a comprehensive three-volume work on the theory of singularities. It focuses on the topological and geometric aspects of singularities and provides a detailed introduction to the subject. Written by V. I. Arnold, S. M. Gusein-Zade, and A. N. Varchenko, the book explores key concepts including: * The definition of a singularity and its relation to the gradient of a function. * The classification of singularities and their topological structure. * The theory of catastrophes and its applications to natural phenomena. * The use of singularities in knot theory and the study of manifolds. * The relation between singularities and intersection theory.