Foundations of differentiable manifolds and Lie groups / Frank W. Warner.
Editor: Glenview, Ill. : Scott, Foresman, c1971Descripción: 270 p. : il. ; 25 cmOtra clasificación: 58A05 (22E15)1 MANIFOLDS Preliminaries [2] Differentiable Manifolds [5] The Second Axiom of Countability [8] Tangent Vectors and Differentials [11] Submanifolds, Diffeomorphisms, and the Inverse Function Theorem [22] Implicit Function Theorems [30] Vector Fields [34] Distributions and the Frobenius Theorem [41] Exercises [50] TENSORS AND DIFFERENTIAL FORMS Tensor and Exterior Algebras [54] Tensor Fields and Differential Forms [62] The Lie Derivative [69] Differential Ideals [73] Exercises [77] 3 LIE GROUPS Lie Groups and Their Lie Algebras [82] Homomorphisms [89] Lie Subgroups [92] Coverings [98] Simply Connected Lie Groups [101] Exponential Map [102] Continuous Homomorphisms [109] Closed Subgroups [110] The Adjoint Representation [112] Automorphisms and Derivations of Bilinear Operations and Forms [117] Homogeneous Manifolds [120] Exercises [132] INTEGRATION ON MANIFOLDS [4] Orientation [138] Integration on Manifolds [140] de Rham Cohomology [153] Exercises [157] SHEAVES, COHOMOLOGY, AND THE DE RHAM THEOREM [5] Sheaves and Presheaves [163] Cochain Complexes [173] Axiomatic Sheaf Cohomology [176] The Classical Cohomology Theories Alexander-Spanier Cohomology [186] de Rham Cohomology [189] Singular Cohomology [191] Čech Cohomology [200] The de Rham Theorem [205] Multiplicative Structure [207] Supports [214] Exercises [216] THE HODGE THEOREM [6] The Laplace-Beltrami Operator [220] The Hodge Theorem [222] Some Calculus [227] Elliptic Operators [240] Reduction to the Periodic Case [243] Ellipticity of the Laplace-Beltrami Operator [250] Exercises [251] BIBLIOGRAPHY [260] INDEX OF NOTATION [262] INDEX [265]
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Bibliografía: p. [260]-261.
1 MANIFOLDS --
Preliminaries [2] --
Differentiable Manifolds [5] --
The Second Axiom of Countability [8] --
Tangent Vectors and Differentials [11] --
Submanifolds, Diffeomorphisms, and the Inverse Function Theorem [22] --
Implicit Function Theorems [30] --
Vector Fields [34] --
Distributions and the Frobenius Theorem [41] --
Exercises [50] --
TENSORS AND DIFFERENTIAL FORMS --
Tensor and Exterior Algebras [54] --
Tensor Fields and Differential Forms [62] --
The Lie Derivative [69] --
Differential Ideals [73] --
Exercises [77] --
3 LIE GROUPS --
Lie Groups and Their Lie Algebras [82] --
Homomorphisms [89] --
Lie Subgroups [92] --
Coverings [98] --
Simply Connected Lie Groups [101] --
Exponential Map [102] --
Continuous Homomorphisms [109] --
Closed Subgroups [110] --
The Adjoint Representation [112] --
Automorphisms and Derivations of Bilinear Operations and Forms [117] --
Homogeneous Manifolds [120] --
Exercises [132] --
INTEGRATION ON MANIFOLDS [4] --
Orientation [138] --
Integration on Manifolds [140] --
de Rham Cohomology [153] --
Exercises [157] --
SHEAVES, COHOMOLOGY, AND THE DE RHAM THEOREM [5] --
Sheaves and Presheaves [163] --
Cochain Complexes [173] --
Axiomatic Sheaf Cohomology [176] --
The Classical Cohomology Theories --
Alexander-Spanier Cohomology [186] --
de Rham Cohomology [189] --
Singular Cohomology [191] --
Čech Cohomology [200] --
The de Rham Theorem [205] --
Multiplicative Structure [207] --
Supports [214] --
Exercises [216] --
THE HODGE THEOREM [6] --
The Laplace-Beltrami Operator [220] --
The Hodge Theorem [222] --
Some Calculus [227] --
Elliptic Operators [240] --
Reduction to the Periodic Case [243] --
Ellipticity of the Laplace-Beltrami Operator [250] --
Exercises [251] --
BIBLIOGRAPHY [260] --
INDEX OF NOTATION [262] --
INDEX [265] --
MR, 45 #4312
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