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58C20 Global analysis, analysis on manifolds -- Calculus on manifolds; nonlinear operators -- Differentiation theory (Gateaux, Fréchet, etc.)

57R45 Manifolds and cell complexes -- Differential topology -- Singularities of differentiable mappings

57R70 Manifolds and cell complexes -- Differential topology -- Critical points and critical submanifolds En-ligne: Numir | Springerlink | Zentralblatt | MathSciNet

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This book is a textbook in contemporary theory of singularities of stable smooth mappings. The first chapters are concerned with the necessary preliminaries: the basic concepts of the theory of manifolds, Sard's theorem and the Malgrange preparation theorem. Further chapters deal with more special questions of the theory of singularities: here we find accounts of Thom's transversality theorem, Morse theory, Mather's theorem on the equivalence of infinitesimal stability and stability, and also results of Mather, Thom, Boardman, Morin and Levine on the classification and canonical forms of singularities. (MathSciNet)

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