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Locally Mixed Symmetric Spaces

  • Book
  • © 2021

Overview

Authors:
  1. Bruce Hunt

    1. RCMB, DZ Bank, Frankfurt am Main, Germany

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  • 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

Part of the book series: Springer Monographs in Mathematics (SMM)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xix
    Download chapter PDF

  2. Symmetric Spaces

    • Bruce Hunt
    Pages 1-177

  3. Locally Symmetric Spaces

    • Bruce Hunt
    Pages 179-319

  4. Locally Mixed Symmetric Spaces

    • Bruce Hunt
    Pages 321-374

  5. Kuga Fiber Spaces

    • Bruce Hunt
    Pages 375-485

  6. Elliptic Surfaces

    • Bruce Hunt
    Pages 487-542

  7. Appendices

    • Bruce Hunt
    Pages 543-598

  8. Back Matter

    Pages 599-622
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Keywords

About this book

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.

Reviews

“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)

Authors and Affiliations

  • RCMB, DZ Bank, Frankfurt am Main, Germany

    Bruce Hunt

About the author

Bruce Hunt studied at the University of Bonn (1978­–1983) and obtained his PhD from the Max Planck Institute für Mathematik in 1986 under Fr. Hirzebruch and Andrew Sommese. From 1987 to 2000 he was Assistant Professor at Purdue University, Göttingen, Kaiserslautern, and the Max Planck Institute. Since 2000 he has worked in international investment banks, in trading architecture and risk control.

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