LEADER 02858nam 2200541 450 001 996466760103316 005 20220912124524.0 010 $a3-540-38494-4 024 7 $a10.1007/BFb0093939 035 $a(CKB)1000000000437085 035 $a(DE-He213)978-3-540-38494-6 035 $a(MiAaPQ)EBC5585204 035 $a(Au-PeEL)EBL5585204 035 $a(OCoLC)1066192533 035 $a(MiAaPQ)EBC6842478 035 $a(Au-PeEL)EBL6842478 035 $a(PPN)155194739 035 $a(EXLCZ)991000000000437085 100 $a20220912d1991 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aHomology of locally semialgebraic spaces /$fHans Delfs 205 $a1st ed. 1991. 210 1$aBerlin, Germany ;$aNew York, New York :$cSpringer-Verlag,$d[1991] 210 4$dİ1991 215 $a1 online resource (X, 138 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1484 311 $a0-387-54615-4 311 $a3-540-54615-4 327 $aAbstract locally semialgebraic spaces -- Sheaf theory on locally semialgebraic spaces -- Semialgebraic Borel-Moore-homology -- Some intersection theory. 330 $aLocally semialgebraic spaces serve as an appropriate framework for studying the topological properties of varieties and semialgebraic sets over a real closed field. This book contributes to the fundamental theory of semialgebraic topology and falls into two main parts. The first dealswith sheaves and their cohomology on spaces which locally look like a constructible subset of a real spectrum. Topics like families of support, homotopy, acyclic sheaves, base-change theorems and cohomological dimension are considered. In the second part a homology theory for locally complete locally semialgebraic spaces over a real closed field is developed, the semialgebraic analogue of classical Bore-Moore-homology. Topics include fundamental classes of manifolds and varieties, Poincare duality, extensions of the base field and a comparison with the classical theory. Applying semialgebraic Borel-Moore-homology, a semialgebraic ("topological") approach to intersection theory on varieties over an algebraically closed field of characteristic zero is given. The book is addressed to researchers and advanced students in real algebraic geometry and related areas. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1484 606 $aAlgebraic spaces 606 $aHomology theory 615 0$aAlgebraic spaces. 615 0$aHomology theory. 676 $a516.35 700 $aDelfs$b Hans$054844 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466760103316 996 $aHomology of locally semialgebraic spaces$978642 997 $aUNISA