Homology of Locally Semialgebraic Spaces

Hans Delfs (Autor)

Buch | Softcover

X, 138 Seiten

1991 | 1991
Springer Berlin (Verlag)
978-3-540-54615-3 (ISBN)

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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.

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

Erscheint lt. Verlag	23.10.1991
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	X, 138 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	234 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
Schlagworte	algebraic topology • cohomology • Homology • Homotopy • real varieties • semialgebraic topology • sheaf theory
ISBN-10	3-540-54615-4 / 3540546154
ISBN-13	978-3-540-54615-3 / 9783540546153
Zustand	Neuware