Lecture Notes in Algebraic Topology 2024 pdf epub mobi 电子书

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发表于2024-05-18

Lecture Notes in Algebraic Topology 2024 pdf epub mobi 电子书

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出版者:American Mathematical Society

作者:Paul Kirk James F. Davis

出品人:

页数:367

译者:

出版时间:2001-8-1

价格:USD 64.00

装帧:Hardcover

isbn号码:9780821821602

丛书系列:Graduate Studies in Mathematics

图书标签: 数学代数拓扑拓扑 topology Math

Lecture Notes in Algebraic Topology 2024 pdf epub mobi 电子书图书描述

The amount of algebraic topology a graduate student specializing in topology must learn can be intimidating. Moreover, by their second year of graduate studies, students must make the transition from understanding simple proofs line-by-line to understanding the overall structure of proofs of difficult theorems.

To help students make this transition, the material in this book is presented in an increasingly sophisticated manner. It is intended to bridge the gap between algebraic and geometric topology, both by providing the algebraic tools that a geometric topologist needs and by concentrating on those areas of algebraic topology that are geometrically motivated.

Prerequisites for using this book include basic set-theoretic topology, the definition of CW-complexes, some knowledge of the fundamental group/covering space theory, and the construction of singular homology. Most of this material is briefly reviewed at the beginning of the book.

The topics discussed by the authors include typical material for first- and second-year graduate courses. The core of the exposition consists of chapters on homotopy groups and on spectral sequences. There is also material that would interest students of geometric topology (homology with local coefficients and obstruction theory) and algebraic topology (spectra and generalized homology), as well as preparation for more advanced topics such as algebraic K-theory and the s-cobordism theorem.

A unique feature of the book is the inclusion, at the end of each chapter, of several projects that require students to present proofs of substantial theorems and to write notes accompanying their explanations. Working on these projects allows students to grapple with the “big picture”, teaches them how to give mathematical lectures, and prepares them for participating in research seminars.

The book is designed as a textbook for graduate students studying algebraic and geometric topology and homotopy theory. It will also be useful for students from other fields such as differential geometry, algebraic geometry, and homological algebra. The exposition in the text is clear; special cases are presented over complex general statements.

Lecture Notes in Algebraic Topology 2024 pdf epub mobi 电子书

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本书解决了我对于同调论中符号表示意义的解答Sq(X;R) =functions({singular simplexes},R).接近现代代数拓扑的研究生课程：范畴函子导出函子作为基本语言；三角剖分拓扑空间同胚与几何表示单复形，相对奇异链复形是自由模；奇异上同调是反变函子空间连续映射到分次模同态，Kronecker pairing 类比域形式微分

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