Homology of Locally Semialgebraic Spaces

  • Authors
  • HansĀ Delfs

Part of the Lecture Notes in Mathematics book series (LNM, volume 1484)

Table of contents

  1. Front Matter
    Pages I-IX
  2. Hans Delfs
    Pages 62-114
  3. Hans Delfs
    Pages 115-129
  4. Back Matter
    Pages 130-136

About this book

Introduction

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.

Keywords

Algebraic topology Cohomology Homotopy homology real varieties semialgebraic topology sheaf theory

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0093939
  • Copyright Information Springer-Verlag Berlin Heidelberg 1991
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-54615-3
  • Online ISBN 978-3-540-38494-6
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book