Homology of Locally Semialgebraic Spaces

Delfs, Hans

ISBN 10: 3540546154 / ISBN 13: 9783540546153

Published by Springer, 1991

Unread book in perfect condition. Seller Inventory # 5906430

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.

Bibliographic Details

Title: Homology of Locally Semialgebraic Spaces
Publisher: Springer
Publication Date: 1991
Binding: Soft cover
Condition: As New