02858nam 2200541 450 99646676010331620220912124524.03-540-38494-410.1007/BFb0093939(CKB)1000000000437085(DE-He213)978-3-540-38494-6(MiAaPQ)EBC5585204(Au-PeEL)EBL5585204(OCoLC)1066192533(MiAaPQ)EBC6842478(Au-PeEL)EBL6842478(PPN)155194739(EXLCZ)99100000000043708520220912d1991 uy 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierHomology of locally semialgebraic spaces /Hans Delfs1st ed. 1991.Berlin, Germany ;New York, New York :Springer-Verlag,[1991]©19911 online resource (X, 138 p.) Lecture Notes in Mathematics,0075-8434 ;14840-387-54615-4 3-540-54615-4 Abstract locally semialgebraic spaces -- Sheaf theory on locally semialgebraic spaces -- Semialgebraic Borel-Moore-homology -- Some intersection theory.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.Lecture Notes in Mathematics,0075-8434 ;1484Algebraic spacesHomology theoryAlgebraic spaces.Homology theory.516.35Delfs Hans54844MiAaPQMiAaPQMiAaPQBOOK996466760103316Homology of locally semialgebraic spaces78642UNISA