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Titlebook: Rational Homotopy Theory and Differential Forms; Phillip Griffiths,John Morgan Book 2013Latest edition Springer Science+Business Media New

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发表于 2025-3-21 16:04:02 | 显示全部楼层 |阅读模式
书目名称Rational Homotopy Theory and Differential Forms
编辑Phillip Griffiths,John Morgan
视频video
概述Second edition with fully updated content.Includes a readable introduction for non-specialists.Provides many elementary examples and exercises
丛书名称Progress in Mathematics
图书封面Titlebook: Rational Homotopy Theory and Differential Forms;  Phillip Griffiths,John Morgan Book 2013Latest edition Springer Science+Business Media New
描述.This completely revised and corrected version of the well-known Florence notes circulated by the authors together with E. Friedlander examines basic topology, emphasizing homotopy theory. Included is a discussion of Postnikov towers and rational homotopy theory. This is then followed by an in-depth look at differential forms and de Tham’s theorem on simplicial complexes. In addition, Sullivan’s results on computing the rational homotopy type from forms is presented.  .New to the Second Edition: .*Fully-revised appendices including an expanded discussion of the Hirsch lemma.*Presentation of a natural proof of a Serre spectral sequence result .*Updated content throughout the book, reflecting advances in the area of homotopy theory.With its modern approach and timely revisions, this second edition of .Rational Homotopy Theory and Differential Forms. will be a valuable resource for graduate students and researchers in algebraic topology, differential forms, and homotopy theory. .
出版日期Book 2013Latest edition
关键词Brouwer‘s theorem; algebraic topology; cohomology; differential forms; homotopy; obstruction theory; ratio
版次2
doihttps://doi.org/10.1007/978-1-4614-8468-4
isbn_softcover978-1-4939-3699-1
isbn_ebook978-1-4614-8468-4Series ISSN 0743-1643 Series E-ISSN 2296-505X
issn_series 0743-1643
copyrightSpringer Science+Business Media New York 2013
The information of publication is updating

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发表于 2025-3-21 20:50:36 | 显示全部楼层
Book 2013Latest editiontopology, emphasizing homotopy theory. Included is a discussion of Postnikov towers and rational homotopy theory. This is then followed by an in-depth look at differential forms and de Tham’s theorem on simplicial complexes. In addition, Sullivan’s results on computing the rational homotopy type fro
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Examples and Computations,consider the third homotopy group of a simply connected space and the homotopy theory of simply connected 4-manifolds. Lastly, we discuss products and Massey products in cohomology, the principle of two types and the formality of compact Kahler manifolds.
发表于 2025-3-22 20:49:44 | 显示全部楼层
Functorality,the p.l. forms on C to that for X is a functorial bijection. We reformulate this result as an equivalence of the rational homotopy category of simply connected spaces with the homotopy category of simply connected DGAs defined over the rationals.
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Introduction,nifold to classical algebra-topological invariants. The next seven chapters are a review of the basics of classical homotopy theory including the Postnikov tower of a space and the localization of a homotopy type at 0, forming its rational homotopy type. Chapters .–. introduce differential forms and
发表于 2025-3-23 07:23:54 | 显示全部楼层
Basic Concepts,e of a fibration is proved. The path space and loop space are introduced. Singular homology and cohomology are defined, and their basic properties are enumerated. Products in homology and cohomology are introduced and Poincar duality is stated. The chapter ends with a brief introduction to the funct
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