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Differential topology. --- 515.16 --- 515.16 Topology of manifolds --- Topology of manifolds --- Differential topology --- Topologie différentielle

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Decompositions of manifolds

Manifolds (Mathematics) --- Decomposition (Mathematics) --- Mathematics --- Probabilities --- Geometry, Differential --- Topology --- 515.16 --- 515.16 Topology of manifolds --- Topology of manifolds

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This elegant book by distinguished mathematician John Milnor, provides a clear and succinct introduction to one of the most important subjects in modern mathematics. Beginning with basic concepts such as diffeomorphisms and smooth manifolds, he goes on to examine tangent spaces, oriented manifolds, and vector fields. Key concepts such as homotopy, the index number of a map, and the Pontryagin construction are discussed. The author presents proofs of Sard's theorem and the Hopf theorem.

Differential topology --- Topologie différentielle --- 515.16 --- Geometry, Differential --- Topology --- Topology of manifolds --- Differential topology. --- 515.16 Topology of manifolds --- Topologie différentielle

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Although Riemann surfaces are a time-honoured field, this book is novel in its broad perspective that systematically explores the connection with other fields of mathematics. It can serve as an introduction to contemporary mathematics as a whole as it develops background material from algebraic topology, differential geometry, the calculus of variations, elliptic PDE, and algebraic geometry. It is unique among textbooks on Riemann surfaces in including an introduction to Teichmüller theory. For this new edition, the author has expanded and rewritten several sections to include additional material and to improve the presentation.

515.16 --- 515.16 Topology of manifolds --- Topology of manifolds --- Riemann surfaces. --- Riemann, surfaces de --- Riemann surfaces --- Surfaces, Riemann --- Functions --- Differential geometry. --- Differential Geometry. --- Differential geometry

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Differential geometry. Global analysis --- Catastrophes (Mathematics) --- Catastrophes (Mathématiques) --- 515.16 --- Differentiable mappings --- Manifolds (Mathematics) --- Singularities (Mathematics) --- Topology of manifolds --- Basic Sciences. Mathematics --- Geometry, Topology --- Catastrophes (Mathematics). --- Geometry, Topology. --- 515.16 Topology of manifolds --- Catastrophes (Mathématiques) --- Catastrophes, Théorie des