Weakly Semialgebraic Spaces. 1st ed. 1989

種類:

電子ブック

責任表示:

by Manfred Knebusch

出版情報:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1989

著者名:

• Knebusch, Manfred.
• SpringerLink (Online service)

シリーズ名:

Lecture Notes in Mathematics ; 1367

ISBN:

9783540460893 [3540460896]    

注記:

Basic theory of weakly semialgebraic spaces -- Patch complexes, and homotopies again -- Homology and cohomology -- Simplicial spaces.
The 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,

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