Foundations of differentiable manifolds and Lie groups / Frank W. Warner.

Por: Warner, Frank W. (Frank Wilson), 1938-Editor: Glenview, Ill. : Scott, Foresman, c1971Descripción: 270 p. : il. ; 25 cmOtra clasificación: 58A05 (22E15)
Contenidos:
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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Libros Libros Instituto de Matemática, CONICET-UNS
Libros ordenados por tema 58 W279 (Browse shelf) Available A-4077

GEOMETRÍA II

Libros Libros Instituto de Matemática, CONICET-UNS
Libros ordenados por tema 58 W279 (Browse shelf) Ej. 2 Checked out 2022-11-04 A-6618

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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