Homology of Locally Semialgebraic Spaces by Hans DelfsHomology of Locally Semialgebraic Spaces by Hans Delfs

Homology of Locally Semialgebraic Spaces

byHans Delfs

Paperback | October 23, 1991

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Locally semialgebraic spaces serve as an appropriateframework for studying the topological properties ofvarieties and semialgebraic sets over a real closed field.This book contributes to the fundamental theory ofsemialgebraic topology and falls into two main parts.The first dealswith sheaves and their cohomology on spaceswhich locally look like a constructible subset of a realspectrum. Topics like families of support, homotopy, acyclicsheaves, base-change theorems and cohomological dimensionare considered.In the second part a homology theory for locally completelocally semialgebraic spaces over a real closed field isdeveloped, the semialgebraic analogue of classicalBore-Moore-homology. Topics include fundamental classes ofmanifolds and varieties, Poincare duality, extensions of thebase field and a comparison with the classical theory.Applying semialgebraic Borel-Moore-homology, a semialgebraic("topological") approach to intersection theory on varietiesover an algebraically closed field of characteristic zero isgiven. The book is addressed to researchers and advancedstudents in real algebraic geometry and related areas.
Title:Homology of Locally Semialgebraic SpacesFormat:PaperbackDimensions:145 pagesPublished:October 23, 1991Publisher:Springer Berlin HeidelbergLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3540546154

ISBN - 13:9783540546153


Table of Contents

Abstract locally semialgebraic spaces.- Sheaf theory on locally semialgebraic spaces.- Semialgebraic Borel-Moore-homology.- Some intersection theory.