Author : Hans Delfs
Publisher : Springer
ISBN 13 : 3540384944
Total Pages : 145 pages
Book Rating : 4.5/5 (43 download)
Book Synopsis Homology of Locally Semialgebraic Spaces by : Hans Delfs
Download or read book Homology of Locally Semialgebraic Spaces written by Hans Delfs and published by Springer. This book was released on 2006-11-14 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.