Topology and geometry for physicists

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Topology and geometry for physicists / Charles Nash, Siddhartha Sen

資料種別:

図書

出版情報:

Mineola, N.Y. : Dover Publications, 2011, c1983

形態:

viii, 311 p. ; 22 cm

シリーズ名:

Dover books on mathematics <BA04873505>

著者名:

ISBN:

9780486478524 [0486478521] (: pbk)

書誌ID:

BB06130371

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注記:

Originally published: New York : Academic Press, 1983
Bibliography: p. 305
Includes index

主題:

MATHEMATICS / Topology bisacsh

言語:

英語

目次情報:

Preface

Basic Notions of Topology and the Value of Topological Reasoning / Chapter 1：

Introduction / 1.1：

Basic topological notions / 1.2：

Homeomorphisms, homotopy and the idea of topological invariants / 1.3：

Topological invariants of compactness and connectedness / 1.4：

Differential Geometry: Manifolds and Differential Forms / 1.5：

Manifolds / 2.1：

Orientability / 2.2：

Calculus on manifolds / 2.3：

Infinite dimensional manifolds / 2.4：

Differentiable structures / 2.5：

The Fundamental Group / Chapter 3：

Definition of the fundamental group / 3.1：

Simplexes and the calculating theorem / 3.3：

Triangulation of a space with examples / 3.4：

Fundamental group of a product XÃ—Y / 3.5：

The Homology Groups / Chapter 4：

Oriented simplexes and the definition of the homology groups / 4.1：

Abelian groups / 4.3：

Relative homology groups / 4.4：

Exact sequences / 4.5：

Torsion, Kunneth formula, Euler-PoincarÃ© formula and singular homology / 4.6：

The Higher Homotopy Groups / Chapter 5：

Definition of higher homotopy groups / 5.1：

Abelian nature of higher homotopy groups / 5.3：

Relative homotopy groups / 5.4：

The exact homotopy sequence / 5.5：

Cohomology and De Rham Cohomology / Chapter 6：

PoincarÃ©'s lemma / 6.1：

General remarks / 6.4：

The cup product / 6.6：

Superiority of cohomology over homology / 6.7：

Fibre Bundles and Further Differential Geometry / Chapter 7：

Fibre bundle / 7.1：

More examples of bundles / 7.3：

When is a bundle trivial? / 7.4：

Sections of bundles and singularities of vector fields / 7.5：

Cutting a bundle down to size: reduction of the group and contraction of the base space / 7.6：

Remarks on almost Hamiltonian and almost complex structures / 7.7：

G-structures on a compact closed manifold M / 7.8：

Lie derivative / 7.9：

Connection and curvature / 7.10：

The connection form and the gauge potential / 7.11：

Parallel transport, covariant derivative and curvature / 7.12：

Covariant exterior derivatives / 7.13：

The Bianchi identities and *F / 7.14：

Connection in the tangent bundle / 7.15：

The torsion tensor / 7.16：

Geodesics / 7.17：

The Levi-Civita connection / 7.18：

The Yang-Mills connection / 7.19：

The Maxwell connection / 7.20：

Characteristic classes / 7.21：

Chern, Pontrjagin and Euler classes / 7.23：

Characteristic classes in terms of curvature and invariant polynomials / 7.24：

Classification of bundles / 7.25：

The Stiefel-Whitney class / 7.26：

Calculation of characteristic classes / 7.27：

Formulae obeyed by characteristic classes / 7.28：

Global invariants and local geometry / 7.30：

Morse Theory / Chapter 8：

More inequalities / 8.1：

Morse lemma / 8.2：

Symmetry breaking selection rules in crystals / 8.3：

Estimating equilibrium positions / 8.4：

Defects, Textures and Homotopy Theory / Chapter 9：

Planar spin in two dimensions / 9.1：

Definition of an ordered medium / 9.2：

Stability of defects theorem / 9.3：

Examples / 9.4：

Yang-Mills Theories: Instantons and Monopoles / 9.5：

Instantons / 10.1：

Topology and boundary conditions / 10.3：

Instantons and absolute minima / 10.4：

The instanton solution / 10.5：

The instanton number and the second Chern class / 10.6：

Multi-instantons / 10.7：

Quaternions and SU(2) connections / 10.8：

The k = 1 instanton in terms of quaternions / 10.9：

Instantons with |k|> 1 and quaternions / 10.10：

Example of instantons with |k|> 1 / 10.11：

Twistor methods and instantons / 10.12：

The projective twistor space / 10.13：

?-planes and anti-self-dual connections / 10.14：

The equivalence between instantons and holomorphic vector bundles / 10.16：

Construction of an instanton given a holomorphic vector bundle / 10.17：

The Minkowski case / 10.18：

Monopoles / 10.19：

The Bohm-Aharanov effect / 10.20：

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