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Differential Geometry, Lie Groups and Symmetric Spaces over General Base Fields and Rings | | Wolfgang Bertram
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8 Feb 2005 | | Subject: | Differential Geometry MSC-class: AMS-classification (2000): 22E65, 53B05, 53C35, 58A05, 58A20, 53B05, 58A32 | math.DG | | Affiliation: | CORIDA Loria Iecn Mmas | | Abstract: | 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 in recent work (collaboration with H. Gloeckner and K.-H. Nee), without any restriction on the dimension or on the characteristic. Two basic features distinguish our 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. | | Source: | arXiv, math.DG/0502168 | | Services: | Forum | Review | PDF | Favorites | |
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