商品描述： 编辑推荐《光滑流形导论(第2版)(英文版)》由世界图书出版公司北京公司出版。作者简介John M. Lee（J.M.李，美国）是国际知名学者，在数学界享有盛誉。本书凝聚了作者多年科研和教学成果，适用于科研工作者、高校教师和研究生。目录1 Smooth Manifolds Topological Manifolds Smooth Structures Examples of Smooth Manifolds Manifolds with Boundary Problems 2 Smooth Maps Smooth Functions and Smooth Maps Partitions of Unity Problems 3 Tangent Vectors Tangent Vectors The Differential of a Smooth Map Computations in Coordinates The Tangent Bundle Velocity Vectors of Curves Alternative Definitions of the Tangent Space Categories and Fur ctors Problems 4 Submersions，Immersions，and Embeddings Maps of Constant Rank Embeddings Submersions Smooth Covering Maps Problems 5 Submanifolds Embedded Submanifolds Immersed Submanifolds Restricting Maps to Submanifolds The Tangent Space to a Submanifold Submanifolds with Boundary Problems 6 Sard's Theorem Sets of Measure Zero Sard's Theorem The Whitney Embedding Theorem The Whitney Approximation Theorems Transversality Problems 7 Lie Groups Basic Definitions Lie Group Homomorphisms Lie Subgroups Group Actions and Equivariant Maps Problems 8 Vector Fields Vector Fields on Manifolds Vector Fields and Smooth Maps Lie Brackets The Lie Algebra of a Lie Group Problems 9 Integral Curves and Flows Integral Curves Flows Flowouts Flows and Flowouts on Manifolds with Boundary Lie Derivatives Commuting Vector Fields Time—Dependent Vector Fields First—Order Partial Differential Equations Problems 10 Vector Bundles Vector Bundles Local and Global Sections of Vector Bundles Bundle Homomorphisms Subbundles Fiber Bundles Problems 11 The Cotangent Bundle Covectors The Differential of a Function Pullbacks of Covector Fields Line Integrals Conservative Covector Fields Problems 12 Tensors Multilinear Algebra Symmetric and Alternating Tensors Tensors and Tensor Fields on Manifolds Problems 13 Riemannian Metrics Riemannian Manifolds The Riemannian Distance Function The Tangent—Cotangent Isomorphism Pseudo—Riemannian Metrics Problems 14 Differential Forms The Algebra of Alternating Tensors Differential Forms on Manifolds Exterior Derivatives Problems 15 Orientations Orientations of Vector Spaces Orientations of Manifolds The Riemannian Volume Form Orientations and Covering Maps Problems 16 Integration on Manifolds The Geometry of Volume Measurement Integration of Differential Forms Stokes's Theorem Manifolds with Corners Integration on Riemannian Manifolds Densities Problems 17 De Rham Cohomology The de Rham Cohomology Groups Homotopy Invariance The Mayer—Vietoris Theorem Degree Theory Proof of the Mayer—Vietoris Theorem Problems 18 Tile de Rham Theorem Singular Homology Singular Cohomology Smooth Singular Homology The de Rham Theorem Problems 19 Distributions and Foliations Distributions and Involutivity The Frobenius Theorem Foliations Lie Subalgebras and Lie Subgroups
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