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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
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Memoirs of the American Mathematical Society
2008; 202 pp; softcover
Volume: 192
ISBN-10: 0-8218-4091-6
ISBN-13: 978-0-8218-4091-7
List Price: US$81 Individual Members: US$48.60
Institutional Members: US\$64.80
Order Code: MEMO/192/900

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.

• Introduction
• Basic notions
• Interpretation of tangent objects via scalar extensions
• Second order differential geometry
• Third and higher order differential geometry
• Lie theory
• Diffeomorphism groups and the exponential jet
• Appendix L. Limitations
• Appendix G. Generalizations
• Appendix: Multilinear geometry
• References