Gregor Fels, Alan Huckleberry, Joseph A. Wolf

Cycle Spaces of Flag Domains (eBook, PDF)

A Complex Geometric Viewpoint

• Format: PDF

Produktbeschreibung

Presents a state-of-the art and systematic examination of cycle spaces of flag domains. Assuming only a basic familiarity with the concepts of Lie theory and geometry, this work presents a complete structure theory for these cycle spaces, as well as their applications to harmonic analysis and algebraic geometry. Driven by numerous examples, the exposition is presented from the complex geometric viewpoint, but the methods, applications and much of the motivation also come from real and complex algebraic groups and their representations, as well as other areas of geometry. All the necessary background material is provided for the nonspecialist, including a good bibliography and index, thus making the book accessible to readers from a wide range of fields. Researchers and graduate students in differential geometry, complex analysis, harmonic analysis, representation theory, transformation groups, algebraic geometry, and areas of global geometric analysis will benefit from this work.

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Produktdetails

• Verlag: Birkhäuser Boston
• Seitenzahl: 339
• Erscheinungstermin: 30. Juli 2006
• Englisch
• ISBN-13: 9780817644796
• Artikelnr.: 37356790

Autorenporträt

Gregor Fels, University of Tübingen, Germany / Alan Huckleberry, University of Bochum, Germany / Joseph A. Wolf, University of California, Berkeley, CA, USA

Inhaltsangabe

Dedication.
- Acknowledgments.
- Introduction.

- Part I: Introduction to Flag Domain Theory.
- Overview.
- Structure of Complex Flag Manifolds.
- Real Group Orbits.
- Orbit Structure for Hermitian Symmetric Spaces.
- Open Orbits.
- The Cycle Space of a Flag Domain.

- Part II: Cycle Spaces as Universal Domains.
- Overview.
- Universal Domains.
- B-Invariant Hypersurfaces in Mz.
- Orbit Duality via Momentum Geometry.
- Schubert Slices in the Context of Duality.
- Analysis of the Boundary of U.
- Invariant Kobayashi Hyperbolic Stein Domains.
- Cycle Spaces of Lower-Dimensional Orbits.
- Examples.

- Part III: Analytic and Geometric Concequences.
- Overview.
- The Double Fibration Transform.
- Variation of Hodge Structure.
- Cycles in the K3 Period Domain.

- Part IV: The Full Cycle Space.
- Overview.
- Combinatorics of Normal Bundles of Base Cycles.
- Methods for Computing H1(C;O(E((q+0q)s

Rezensionen

From the reviews:

"Cycle spaces can be a useful tool in the study of real semisimple Lie groups, and the research monograph which is reviewed here is devoted to describing their features. The exposition ... is in principle self-contained for a good graduate reader, who will also find a wealth of concrete examples. ... the approach used by the authors throughout this monograph is based on a combination of group-theoretical methods ... the result is an intriguing melting pot, opening interesting perspectives of interaction among different research branches." (Corrado Marastoni, Mathematical Reviews, Issue 2006 h)

"A systematic exposition of the background, methods, and recent results in the theory of cycle spaces of flag domains. ... The value of this progress in mathematics volume to a wide group of researchers ... is indisputable. They all will admire the volume for the many new results presented for the first time. Your reviewer would strongly recommend that you spend a few hours with this volume long enough to familiarize yourself with its contents. You'll be back for the details when you need them." (Current Engineering Practice, Vol. 48, 2005-2006)