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

Autorentext

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.

Inhalt
Introduction.- Symmetric Spaces.- Locally Symmetric Spaces.- Locally mixed symmetric spaces.- Kuga fiber spaces.- Elliptic surfaces.- Appendices.