Analysis of Rings and Manifolds
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Preface
The book aims to give a detailed theory of tools in analysis that are used to study problems involving (not necessarily unital) rings (e.g., Banach algebras) and differentiable or complex-analytic manifolds. The first chapter covers basics of point-set topology and set theory that are needed in the subsequent chapters. For more detailed accounts the readers are referred to other books such as Topology. The appendix contains a chapter on graduate-level (commutative) algebraic materials (e.g., field extension, associate algebra, multilinear algebra) that are needed, for example, for the study of Lie algebras.
Contents
- Chapter 1. Topological groups
(October, 2009) - Filters -Topological spaces - Compact sets and Hausdorff spaces - Topological groups - Metric spaces - Continuous functions on a compact space
- Chapter 2. Non-commutative rings
(October, 2009) - Jacobson radical
- Chapter 3. Lie algebras (October, 2009)
- Chapter 4. Differentiable manifolds (October, 2009)
- integrable manifolds, Lie groups
- Chapter 5. Complex and symplectic geometries (October, 2009)
- Kähler manifolds, Lagrangian submanifolds
- Chapter 5. Representations of compact groups (October, 2009)
- Appendices (October, 2009)
- Set theory - Commutative algebra - Differential analysis
