Locally Mixed Symmetric Spaces
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Beschreibung
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.
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.
Introduces locally mixed symmetric spaces with an emphasis on geometric concepts and relations Focuses on examples, avoiding technicalities and assuming only a working knowledge of real Lie groups Includes two chapters on Kuga fiber spaces and elliptic surfaces
Autor*in
Bruce Hunt
Themen in »Locally Mixed Symmetric Spaces«
symmetric space discrete arithmetic Lie group fiber space fiber bundle arithmetic group Shimura variety
Stimmen zu »Locally Mixed Symmetric Spaces«
“The book contains a very useful index. As a global view, we must mention that most of the results are given with their complete proofs; this fact increases the value of the book and makes it an excellent scientific material for the researchers in the field. Besides the valuable contents, the topics being of high interest for specialists in topology, algebraic and differential geometry, one must remark once more the very well organization and clarity of this monograph.” (Adela-Gabriela Mihai, zbMATH 1504.53001, 2023)
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