Download or read book Differential Geometry, Lie Groups, and Symmetric Spaces Over General Base Fields and Rings written by Wolfgang Bertram and published by American Mathematical Society(RI). This book was released on 2014-09-11 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.