| 书目名称 | Weakly Semialgebraic Spaces | | 编辑 | Manfred Knebusch | | 视频video | | | 丛书名称 | Lecture Notes in Mathematics | | 图书封面 |  | | 描述 | 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, 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 t | | 出版日期 | Book 1989 | | 关键词 | Algebraic topology; Homotopy; algebra; cohomology; homology; homotopie | | 版次 | 1 | | doi | https://doi.org/10.1007/BFb0084987 | | isbn_softcover | 978-3-540-50815-1 | | isbn_ebook | 978-3-540-46089-3Series ISSN 0075-8434 Series E-ISSN 1617-9692 | | issn_series | 0075-8434 | | copyright | Springer-Verlag Berlin Heidelberg 1989 |
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发表于 2025-3-21 16:04:51
