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Differential geometry. Global analysis --- 515.1 --- Topology --- 515.1 Topology --- Singularités (Mathématiques) --- Differential topology --- Topologie différentielle --- Manifolds (Mathematics) --- Variétés (mathématiques) --- Singularities (Mathematics) --- Singularités (mathématiques) --- Differentiable mappings --- Applications différentiables --- Topologie différentielle. --- Applications différentiables. --- Variétés (mathématiques) --- Applications différentiables. --- Singularités (mathématiques) --- Topologie différentielle.

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Even the simplest singularities of planar curves, e.g. where the curve crosses itself, or where it forms a cusp, are best understood in terms of complex numbers. The full treatment uses techniques from algebra, algebraic geometry, complex analysis and topology and makes an attractive chapter of mathematics, which can be used as an introduction to any of these topics, or to singularity theory in higher dimensions. This book is designed as an introduction for graduate students and draws on the author's experience of teaching MSc courses; moreover, by synthesising different perspectives, he gives a novel view of the subject, and a number of new results.

Singularities (Mathematics) --- Curves, Plane --- Singularités (Mathématiques) --- Courbes planes --- Congresses --- Congrès --- 512.7 --- Algebraic geometry. Commutative rings and algebras --- 512.7 Algebraic geometry. Commutative rings and algebras --- Singularités (Mathématiques) --- Congrès --- Higher plane curves --- Plane curves --- Congresses. --- Curves, Plane. --- Geometry, Algebraic

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Algebraic topology