Locally Mixed Symmetric Spaces

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 giv...

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Bibliographic Details
Main Author: Hunt, Bruce
Format: eBook
Language:English
Published: Cham Springer International Publishing 2021, 2021
Edition:1st ed. 2021
Series:Springer Monographs in Mathematics
Subjects:
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
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300 |a XIX, 622 p. 48 illus., 11 illus. in color  |b online resource 
505 0 |a Introduction -- Symmetric Spaces -- Locally Symmetric Spaces -- Locally mixed symmetric spaces -- Kuga fiber spaces -- Elliptic surfaces -- Appendices 
653 |a Differential geometry 
653 |a Hyperbolic geometry 
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653 |a Topological groups 
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653 |a Hyperbolic Geometry 
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520 |a 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