#manifolds
58. Global Analysis, Analysis on Manifolds
This volume studies analysis on manifolds, combining differential geometry, functional analysis, and partial differential equations. It focuses on global properties of differential operators and geometric structures. Part I. Foundations Chapter 1. Manifolds and Smooth Structures 1.1 Smooth manifolds 1.2 Charts and atlases 1.3 Smooth maps 1.4 Examples 1.5 Basic properties Chapter 2. Vector Bundles 2.1 Definitions 2.2 Sections 2.3 Bundle maps 2.4 Examples 2.5 Applications Chapter 3. Differential Operators 3.1...
57. Manifolds and Cell Complexes
This volume studies manifolds and combinatorial models such as CW complexes. It connects topology, geometry, and algebraic topology through structured spaces. Part I. Topological Manifolds Chapter 1. Definitions and Examples 1.1 Topological manifolds 1.2 Local Euclidean structure 1.3 Charts and atlases 1.4 Examples 1.5 Basic properties Chapter 2. Maps Between Manifolds 2.1 Continuous maps 2.2 Homeomorphisms 2.3 Embeddings 2.4 Submanifolds 2.5 Examples Chapter 3. Topological Properties 3.1 Compactness 3.2 Connectedness...