Singularities of Mappings: The Local Behaviour of Smooth and Complex Analytic Mappings (Grundlehren der mathematischen Wissenschaften)

Preface
Contents
1 Introduction
	1.1 Real or Complex?
	1.2 Structure of the Book
	1.3 The Nearby Stable Object
	1.4 Exercises and Open Questions
	1.5 Notation
Part I Thom-Mather Theory: Right-Left Equivalence, Stability, Versal Unfoldings, Finite Determinacy
	2 Manifolds and Smooth Mappings
		2.1 Germs
		2.2 Manifolds and Their Tangent Spaces
			Exercises for Sect.2.2
		2.3 Inverse Mapping Theorem and Consequences
			Exercises for Sect.2.3
		2.4 Submanifolds
			Exercises for Sect.2.4
		2.5 Vector Fields and Flows
			Exercises for Sect.2.5
		2.6 Transversality
			Exercises for Sect.2.6
		2.7 Local Conical Structure
	3 Left-Right Equivalence and Stability
		3.1 Classification of Functions by Right Equivalence
			Exercises for Sect.3.1
		3.2 Left-Right Equivalence and Stability
			3.2.1 Right Equivalence and Left Equivalence
			Exercises for Sect.3.2
		3.3 First Calculations
			Exercises for Sect.3.3
		3.4 Multi-Germs
			3.4.1 Notation
			Exercises for Sect.3.4
		3.5 Infinitesimal Stability Implies Stability
			Exercises for Sect.3.5
		3.6 Stability of Multi-Germs
			Exercises for Sect.3.6
	4 Contact Equivalence
		4.1 The Contact Tangent Space
		4.2 Using TKef to Calculate TAef
			Exercises for Sect.4.2
		4.3 Construction of Stable Germs as Unfoldings
			Exercises for Sect.4.3
		4.4 Contact Equivalence
			Exercises for Sect.4.4
		4.5 Geometric Criterion for Finite Ae-Codimension
			4.5.1 Sheafification
			Exercises for Sect.4.5
		4.6 Transversality
		4.7 Thom–Boardman Singularities
			Exercises for Sect.4.7
	5 Versal Unfoldings
		5.1 Versality
			Exercises for Sect.5.1
		5.2 Global Stability of C∞ Mappings
			5.2.1 Stable Maps Are Not Always Dense
			5.2.2 Mather\'s Nice Dimensions
		5.3 Topological Stability
		5.4 Bifurcation Sets
			Exercises for Sect.5.4
		5.5 The Notion of Stable Perturbation of a Map-Germ
	6 Finite Determinacy
		6.1 Proof of the Finite Determinacy Theorem
			Exercises for Sect.6.1
		6.2 Estimates for the Determinacy Degree
		6.3 Determinacy and Unipotency
			6.3.1 Unipotent Affine Algebraic Groups
			6.3.2 Unipotent Groups of k-Jets of Diffeomorphisms
			6.3.3 When Is a Closed Affine Space of Germs Contained in a G-Orbit?
			6.3.4 Complexification and Determinacy Degrees
			6.3.5 Notes
		6.4 Complete Transversals
			Exercises for Sect.6.4
		6.5 Notes and Further Developments
	7 Classification of Stable Germs by Their Local Algebras
		7.1 Stable Germs Are Classified by Their Local Algebras
			Exercises for Sect.7.1
		7.2 Construction of Stable Germs as Unfoldings
			Exercises for Sect.7.2
		7.3 The Isosingular Locus
			7.3.1 Weighted Homogeneity and Local Quasihomogeneity
		7.4 Quasihomogeneity and the Nice Dimensions
			7.4.1 Multi-Germs
			7.4.2 The Case n≥p
			7.4.3 The Case n