Homology of Locally Semialgebraic Spaces (Lecture Notes in Mathematics, 1484, Band 1484)

Delfs, Hans

ISBN 10: 3540546154 ISBN 13: 9783540546153

Verlag: Springer Berlin Heidelberg, 2010

Inhaltsangabe

Locally semialgebraic spaces serve as an appropriate framework for studying the topological properties of varieties and semialgebraic sets over a real closed field. This book contributes to the fundamental theory of semialgebraic topology and falls into two main parts. The first dealswith sheaves and their cohomology on spaces which locally look like a constructible subset of a real spectrum. Topics like families of support, homotopy, acyclic sheaves, base-change theorems and cohomological dimension are considered. In the second part a homology theory for locally complete locally semialgebraic spaces over a real closed field is developed, the semialgebraic analogue of classical Bore-Moore-homology. Topics include fundamental classes of manifolds and varieties, Poincare duality, extensions of the base field and a comparison with the classical theory. Applying semialgebraic Borel-Moore-homology, a semialgebraic ("topological") approach to intersection theory on varieties over an algebraically closed field of characteristic zero is given. The book is addressed to researchers and advanced students in real algebraic geometry and related areas.

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Über die Autorin bzw. den Autor

Prof. Dr. Hans Delfs is a member of the Dept. of Computer Science at the Technische Hochschule Nürnberg Georg Simon Ohm. His research and teaching interests include cryptography and information security, database design, and software architectures. Prof. Dr. Helmut Knebl is a member of the Dept. of Computer Science at the Technische Hochschule Nürnberg Georg Simon Ohm. His research and teaching interests include cryptography and information security, algorithms, and theoretical computer science.

Details zur Ausgabe

• Verlag: Springer Berlin Heidelberg
• Erscheinungsdatum: 2010
• Sprache: Englisch
• ISBN 10: 3540546154
• ISBN 13: 9783540546153
• Einband: Broschiert
• Anzahl der Seiten: 148
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