Homology of Locally Semialgebraic Spaces: 1484 (Lecture Notes in Mathematics, 1484) - Softcover

Delfs, Hans

Softcover

ISBN 10: 3540546154 ISBN 13: 9783540546153

Publisher: Springer, 1991

Synopsis

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.

Edition details

• Publisher: Springer
• Publication date: 1991
• Language: English
• ISBN 10: 3540546154
• ISBN 13: 9783540546153
• Binding: Perfect Paperback
• Number of pages: 148