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The Riemann Legacy

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Cover of 'The Riemann Legacy'

Table of Contents

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    Book Overview
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    Chapter 1 Gauss Inner Curvature of Surfaces
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    Chapter 2 Sectional Curvature. Spaces of Constant Curvature. Weyl Hypothesis
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    Chapter 3 Cohomology of Riemann spaces. Theorems of de Rham, Hodge, Kodaira
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    Chapter 4 Chern-Gauss-Bonnet theorem
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    Chapter 5 Curvature and Topology or Characteristic Forms of Chern, Pontriagin, and Euler
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    Chapter 6 Kähler Spaces. Bergman Metrics. Harish-Chandra-Cartan Theorem. Siegel Space (once again!)
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    Chapter 7 Differentiable Structures. Tangent Spaces. Vector Fields
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    Chapter 8 Projective (Inverse) Limits of Topological Spaces
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    Chapter 9 Inductive Limits. Presheaves. Covering Defined by Presheaf
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    Chapter 10 Algebras. Groups, Tensors, Clifford, Grassmann, and Lie Algebras. Theorems of Bott-Milnor, Wedderburn, and Hurwitz
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    Chapter 11 Fields and their Extensions
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    Chapter 12 Galois Theory. Solvable Groups
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    Chapter 13 Ruler and Compass Constructions. Cyclotomic Fields. Kronecker-Weber Theorem
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    Chapter 14 Algebraic and Transcendental Elements
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    Chapter 15 Weyl principle
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    Chapter 16 Topology of Compact Lie Groups
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    Chapter 17 Representations of Compact Lie Groups
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    Chapter 18 Nilpotent, Semimple, and Solvable Lie Algebras
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    Chapter 19 Reflections, Roots, and Weights. Coxeter and Weyl groups
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    Chapter 20 Covariant Differentiation. Parallel Transport. Connections
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    Chapter 21 Remarks on Rich Mathematical Structures of Simple Notions of Physics Based on Example of Analytical Mechanics
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    Chapter 22 Tangent Bundle TM . Vector, Fiber, Tensor and Tensor Densities, and Associate Bundles
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    Chapter 23 G -spaces. Group Representations
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    Chapter 24 Principal and Associated Bundles
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    Chapter 25 Induced Representations and Associated Bundles
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    Chapter 26 Vector Bundles and Locally Free Sheaves
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    Chapter 27 Axiom of Covering Homotopy
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    Chapter 28 Serre Fibering. General Theory of Connection. Corollaries
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    Chapter 29 Homology. Cohomology. de Rham Cohomology
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    Chapter 30 Cohomology of Sheaves. Abstract de Rham Theorem
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    Chapter 31 Homotopy Group π k ( X , x 0 ). Hopf Fibering. Serre Theorem on Exact Sequence of Homotopy Groups of a Fibering
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    Chapter 32 Various Benefits of Characteristic Classes (Orientability, Spin Structures). Clifford Groups, Spin Group
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    Chapter 33 Divisors and Line Bundles. Algebraic and Abelian Varieties
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    Chapter 34 General Abelian Varieties and Theta Function
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    Chapter 35 Theorems on Algebraic Dependence
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    Chapter 36 The Idea of the Riemann Surface
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    Chapter 37 Introduction
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    Chapter 38 The Plateau Problem
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    Chapter 39 Teichmüller Theory. Riemann Moduli Problem
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    Chapter 40 Riemannian Approach to Teichmüller Theory. Harmonic Maps and Teichmüller Space
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    Chapter 41 Teichmüller theory and Plateau-Douglas problem
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    Chapter 42 Rescuing Riemann’s Dirichlet Principle. Potential Theory
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    Chapter 43 The Royal Road to Calculus of Variations (Constantin Carathéodory)
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    Chapter 44 Symplectic and Contact Geometries. Conservation Laws
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    Chapter 45 Direct Methods in Calculus of Variations for Manifolds with Isometries. Equivariant Sobolev Theorems. Yamabe Problem and its Relation to General Relativity
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    Chapter 46 Introduction
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    Chapter 47 On Complex Analysis in Several Variables
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    Chapter 48 Ellipticity, Runge Property, and Runge Type Theorems
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    Chapter 49 Hörmander Method in Complex Analysis
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    Chapter 50 Wirtinger Theorems. Metric Theory of Analytic Sets
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    Chapter 51 The Problem of Poincaré and the Cousin Problems
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    Chapter 52 Ringed Spaces and General Complex Spaces
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    Chapter 53 Construction of Complex Spaces by Gluing and by Taking Quotient
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    Chapter 54 Differential Geometry of Holomorphic Vector Bundles over Compact Riemann Surfaces and Kähler manifolds. Stable Vector Bundles, Hermite-Einstein Connections, and their Moduli Spaces
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    Chapter 55 Introduction
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    Chapter 56 The Riemann ζ function
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    Chapter 57 Hecke Theory
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    Chapter 58 Dedekind ζ K function for number field K and Selberg ζ function
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    Chapter 59 Concluding Remarks
Overall attention for this book and its chapters
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Title
The Riemann Legacy
Published by
Springer Netherlands, April 2013
DOI 10.1007/978-94-015-8939-0
ISBNs
978-9-04-814876-9, 978-9-40-158939-0
Authors

Maurin, Krzysztof

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The data shown below were compiled from readership statistics for 6 Mendeley readers of this research output. Click here to see the associated Mendeley record.

Geographical breakdown

Country Count As %
Unknown 6 100%

Demographic breakdown

Readers by professional status Count As %
Other 1 17%
Student > Doctoral Student 1 17%
Professor 1 17%
Student > Ph. D. Student 1 17%
Researcher 1 17%
Other 1 17%
Readers by discipline Count As %
Physics and Astronomy 3 50%
Mathematics 2 33%
Environmental Science 1 17%