| 000 | 03326nam a22004815i 4500 | ||
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| 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 |
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| 024 | 7 |
_a10.1007/BFb0084987 _2doi |
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| 050 | 4 | _aQA564-609 | |
| 072 | 7 |
_aPBMW _2bicssc |
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| 072 | 7 |
_aMAT012010 _2bisacsh |
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| 072 | 7 |
_aPBMW _2thema |
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| 082 | 0 | 4 |
_a516.35 _223 |
| 100 | 1 |
_aKnebusch, Manfred. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
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| 245 | 1 | 0 |
_aWeakly Semialgebraic Spaces _h[electronic resource] / _cby Manfred Knebusch. |
| 264 | 1 |
_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg : _bImprint: Springer, _c1989. |
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| 300 |
_aCD, 378 p. _bonline resource. |
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| 336 |
_atext _btxt _2rdacontent |
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| 337 |
_acomputer _bc _2rdamedia |
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| 338 |
_aonline resource _bcr _2rdacarrier |
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| 347 |
_atext file _bPDF _2rda |
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| 490 | 1 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v1367 |
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| 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 |
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| 856 | 4 | 0 | _uhttps://doi.org/10.1007/BFb0084987 |
| 912 | _aZDB-2-SMA | ||
| 912 | _aZDB-2-LNM | ||
| 912 | _aZDB-2-BAE | ||
| 999 |
_c10225 _d10225 |
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