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Titlebook: Elements of Homotopy Theory; George W. Whitehead Textbook 1978 The Editor(s) (if applicable) and The Author(s), under exclusive license to

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書目名稱Elements of Homotopy Theory
編輯George W. Whitehead
視頻videohttp://file.papertrans.cn/308/307594/307594.mp4
叢書名稱Graduate Texts in Mathematics
圖書封面Titlebook: Elements of Homotopy Theory;  George W. Whitehead Textbook 1978 The Editor(s) (if applicable) and The Author(s), under exclusive license to
描述As the title suggests, this book is concerned with the elementary portion of the subject of homotopy theory. It is assumed that the reader is familiar with the fundamental group and with singular homology theory, including the Universal Coefficient and Kiinneth Theorems. Some acquaintance with manifolds and Poincare duality is desirable, but not essential. Anyone who has taught a course in algebraic topology is familiar with the fact that a formidable amount of technical machinery must be introduced and mastered before the simplest applications can be made. This phenomenon is also observable in the more advanced parts of the subject. I have attempted to short-circuit it by making maximal use of elementary methods. This approach entails a leisurely exposition in which brevity and perhaps elegance are sacrificed in favor of concreteness and ease of application. It is my hope that this approach will make homotopy theory accessible to workers in a wide range of other subjects-subjects in which its impact is beginning to be felt. It is a consequence of this approach that the order of development is to a certain extent historical. Indeed, if the order in which the results presented here
出版日期Textbook 1978
關(guān)鍵詞Base; Calc; Characteristic class; Elements; Excision theorem; Fundamental group; Homotopie; Homotopy; Homoto
版次1
doihttps://doi.org/10.1007/978-1-4612-6318-0
isbn_softcover978-1-4612-6320-3
isbn_ebook978-1-4612-6318-0Series ISSN 0072-5285 Series E-ISSN 2197-5612
issn_series 0072-5285
copyrightThe Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Science+Busines
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Homology with Local Coefficients,e of the last chapter. If . → . is a cross-section over the .-skeleton, the problem of extending . reduces to a family of local problems: for each . + l)-cell . of ., the induced fibration over Δ. is fibre homotopically trivial. Its total space may thus be represented as a product Δ. x ., where . is
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Homology of Fibre Spaces: Elementary Theory,. The behavior of the homology groups is much more complicated. In the simplest case, that of a trivial fibration, the relationship is given by the Kimneth Theorem. The general case will be treated in Chapter XIII with the aid of the complicated machinery of spectral sequences. In this Chapter we sh
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