Format:
1 Online-Ressource (XIX, 622 p. 48 illus., 11 illus. in color.)
ISBN:
9783030698041
Series Statement:
Springer Monographs in Mathematics
Content:
Introduction -- Symmetric Spaces -- Locally Symmetric Spaces -- Locally mixed symmetric spaces -- Kuga fiber spaces -- Elliptic surfaces -- Appendices.
Content:
What do the classification of algebraic surfaces, Weyl's dimension formula and maximal orders in central simple algebras have in common? All are related to a type of manifold called locally mixed symmetric spaces in this book. The presentation emphasizes geometric concepts and relations and gives each reader the "roter Faden", starting from the basics and proceeding towards quite advanced topics which lie at the intersection of differential and algebraic geometry, algebra and topology. Avoiding technicalities and assuming only a working knowledge of real Lie groups, the text provides a wealth of examples of symmetric spaces. The last two chapters deal with one particular case (Kuga fiber spaces) and a generalization (elliptic surfaces), both of which require some knowledge of algebraic geometry. Of interest to topologists, differential or algebraic geometers working in areas related to arithmetic groups, the book also offers an introduction to the ideas for non-experts.
Additional Edition:
ISBN 9783030698034
Additional Edition:
ISBN 9783030698058
Additional Edition:
ISBN 9783030698065
Additional Edition:
Erscheint auch als Druck-Ausgabe ISBN 9783030698058
Additional Edition:
Erscheint auch als Druck-Ausgabe ISBN 9783030698065
Additional Edition:
Erscheint auch als Druck-Ausgabe Hunt, Bruce, 1958 - Locally mixed symmetric spaces Cham : Springer, 2021 ISBN 9783030698034
Language:
English
DOI:
10.1007/978-3-030-69804-1
