| 書目名稱 | Lectures on Algebraic Topology | | 編輯 | Albrecht Dold | | 視頻video | http://file.papertrans.cn/584/583473/583473.mp4 | | 叢書名稱 | Grundlehren der mathematischen Wissenschaften | | 圖書封面 |  | | 描述 | This is essentially a book on singular homology and cohomology with special emphasis on products and manifolds. It does not treat homotopy theory except for some basic notions, some examples, and some applica- tions of (co-)homology to homotopy. Nor does it deal with general(-ised) homology, but many formulations and arguments on singular homology are so chosen that they also apply to general homology. Because of these absences I have also omitted spectral sequences, their main applications in topology being to homotopy and general (co-)homology theory. Cech- cohomology is treated in a simple ad hoc fashion for locally compact subsets of manifolds; a short systematic treatment for arbitrary spaces, emphasizing the universal property of the Cech-procedure, is contained in an appendix. The book grew out of a one-year‘s course on algebraic topology, and it can serve as a text for such a course. For a shorter basic course, say of half a year, one might use chapters II, III, IV (§§ 1-4), V (§§ 1-5, 7, 8), VI (§§ 3, 7, 9, 11, 12). As prerequisites the student should know the elementary parts of general topology, abelian group theory, and the language of categories - although our chapter | | 出版日期 | Book 19721st edition | | 關(guān)鍵詞 | Algebraic; Algebraic topology; Homotopy; Topology; cohomology; group theory; homology; homotopy theory | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-662-00756-3 | | isbn_ebook | 978-3-662-00756-3Series ISSN 0072-7830 Series E-ISSN 2196-9701 | | issn_series | 0072-7830 | | copyright | Springer-Verlag Berlin Heidelberg 1972 |
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