000 03326nam a22004815i 4500
001 978-3-540-46089-3
003 DE-He213
005 20190213151316.0
007 cr nn 008mamaa
008 121227s1989 gw | s |||| 0|eng d
020 _a9783540460893
_9978-3-540-46089-3
024 7 _a10.1007/BFb0084987
_2doi
050 4 _aQA564-609
072 7 _aPBMW
_2bicssc
072 7 _aMAT012010
_2bisacsh
072 7 _aPBMW
_2thema
082 0 4 _a516.35
_223
100 1 _aKnebusch, Manfred.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aWeakly Semialgebraic Spaces
_h[electronic resource] /
_cby Manfred Knebusch.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c1989.
300 _aCD, 378 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1367
505 0 _aBasic theory of weakly semialgebraic spaces -- Patch complexes, and homotopies again -- Homology and cohomology -- Simplicial spaces.
520 _aThe book is the second part of an intended three-volume treatise on semialgebraic topology over an arbitrary real closed field R. In the first volume (LNM 1173) the category LSA(R) or regular paracompact locally semialgebraic spaces over R was studied. The category WSA(R) of weakly semialgebraic spaces over R - the focus of this new volume - contains LSA(R) as a full subcategory. The book provides ample evidence that WSA(R) is "the" right cadre to understand homotopy and homology of semialgebraic sets, while LSA(R) seems to be more natural and beautiful from a geometric angle. The semialgebraic sets appear in LSA(R) and WSA(R) as the full subcategory SA(R) of affine semialgebraic spaces. The theory is new although it borrows from algebraic topology. A highlight is the proof that every generalized topological (co)homology theory has a counterpart in WSA(R) with in some sense "the same", or even better, properties as the topological theory. Thus we may speak of ordinary (=singular) homology groups, orthogonal, unitary or symplectic K-groups, and various sorts of cobordism groups of a semialgebraic set over R. If R is not archimedean then it seems difficult to develop a satisfactory theory of these groups within the category of semialgebraic sets over R: with weakly semialgebraic spaces this becomes easy. It remains for us to interpret the elements of these groups in geometric terms: this is done here for ordinary (co)homology.
650 0 _aGeometry, algebraic.
650 0 _aAlgebraic topology.
650 1 4 _aAlgebraic Geometry.
_0http://scigraph.springernature.com/things/product-market-codes/M11019
650 2 4 _aAlgebraic Topology.
_0http://scigraph.springernature.com/things/product-market-codes/M28019
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783662212516
776 0 8 _iPrinted edition:
_z9783540508151
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1367
856 4 0 _uhttps://doi.org/10.1007/BFb0084987
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c10225
_d10225