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Analysis, Manifolds and Physics Part I: Basics
This reference book, which has found wide use as a text, provides an answer to the needs of graduate physical mathematics students and their teachers. The present edition is a thorough revision of the first, including a new chapter entitled ``Connections on Principle Fibre Bundles'' which includes sections on holonomy, characteristic classes, invariant curvature integrals and problems on the geometry of gauge fields, monopoles, instantons, spin structure and spin connections. Many paragraphs have been rewritten, and examples and exercises added to ease the study of several chapters. The index includes over 130 entries.
Preface. Chapters: I. Review of fundamental notions of analysis. II. Differential calculus on Banach spaces. III. Differentiable manifolds, finite dimensional case. IV. Integration on manifolds. V. Riemannian manifolds. Kählerian manifolds. V bis. Connections on a principle fibre bundle. VI. Distributions. VII. Differentiable manifolds, infinite dimensional case. References. Symbols. Index. Series: Analysis, Manifolds and Physics