Lecture Notes in Mathematics

Homology of Locally Semialgebraic Spaces

Authors: Delfs, Hans

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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.

Table of contents (4 chapters)

Table of contents (4 chapters)

Buy this book

eBook $29.99
price for USA in USD
  • ISBN 978-3-540-38494-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $39.99
price for USA in USD
  • ISBN 978-3-540-54615-3
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Homology of Locally Semialgebraic Spaces
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1484
Copyright
1991
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-38494-6
DOI
10.1007/BFb0093939
Softcover ISBN
978-3-540-54615-3
Series ISSN
0075-8434
Edition Number
1
Number of Pages
X, 138
Topics