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Differential Geometry, Lie Groups and Symmetric Spaces over General Base Fields and Rings
 
Wolfgang Bertram Université Henri Poincaré (Nancy I), Vandœuvre-lés-Nancy, France
Differential Geometry, Lie Groups and Symmetric Spaces over General Base Fields and Rings
eBook ISBN:  978-1-4704-0506-9
Product Code:  MEMO/192/900.E
List Price: $81.00
MAA Member Price: $72.90
AMS Member Price: $48.60
Differential Geometry, Lie Groups and Symmetric Spaces over General Base Fields and Rings
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Differential Geometry, Lie Groups and Symmetric Spaces over General Base Fields and Rings
Wolfgang Bertram Université Henri Poincaré (Nancy I), Vandœuvre-lés-Nancy, France
eBook ISBN:  978-1-4704-0506-9
Product Code:  MEMO/192/900.E
List Price: $81.00
MAA Member Price: $72.90
AMS Member Price: $48.60
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1922008; 202 pp
    MSC: Primary 22; 53; 58; Secondary 14; 15; 51

    The aim of this work is to lay the foundations of differential geometry and Lie theory over the general class of topological base fields and -rings for which a differential calculus has been developed, without any restriction on the dimension or on the characteristic. Two basic features distinguish the author's approach from the classical real (finite or infinite dimensional) theory, namely the interpretation of tangent- and jet functors as functors of scalar extensions and the introduction of multilinear bundles and multilinear connections which generalize the concept of vector bundles and linear connections.

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • I. Basic notions
    • II. Interpretation of tangent objects via scalar extensions
    • III. Second order differential geometry
    • IV. Third and higher order differential geometry
    • V. Lie theory
    • VI. Diffeomorphism groups and the exponential jet
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1922008; 202 pp
MSC: Primary 22; 53; 58; Secondary 14; 15; 51

The aim of this work is to lay the foundations of differential geometry and Lie theory over the general class of topological base fields and -rings for which a differential calculus has been developed, without any restriction on the dimension or on the characteristic. Two basic features distinguish the author's approach from the classical real (finite or infinite dimensional) theory, namely the interpretation of tangent- and jet functors as functors of scalar extensions and the introduction of multilinear bundles and multilinear connections which generalize the concept of vector bundles and linear connections.

  • Chapters
  • Introduction
  • I. Basic notions
  • II. Interpretation of tangent objects via scalar extensions
  • III. Second order differential geometry
  • IV. Third and higher order differential geometry
  • V. Lie theory
  • VI. Diffeomorphism groups and the exponential jet
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.