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Homology of Locally Semialgebraic Spaces

  • Book
  • © 1991

Overview

Authors:
  1. Hans Delfs
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1484)

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Table of contents (4 chapters)

  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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Keywords

About this book

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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