Homology of Locally Semialgebraic Spaces

1. Front Matter

   Pages I-IX

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2. Abstract locally semialgebraic spaces

   • Hans Delfs

   Pages 1-16

3. Sheaf theory on locally semialgebraic spaces

   • Hans Delfs

   Pages 17-61

4. Semialgebraic Borel-Moore-homology

   • Hans Delfs

   Pages 62-114

5. Some intersection theory

   • Hans Delfs

   Pages 115-129

6. Back Matter

   Pages 130-136

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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.

• Algebraic topology
• Cohomology
• Homotopy
• homology
• real varieties
• semialgebraic topology
• sheaf theory

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