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# ðŸ“™ Lecture notes in algebraic topology by Paul Kirk James F. Davis â€” free download

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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

## About book:

## About file:

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- Series:
**Graduate Studies in Mathematics 035** - Author:
**Paul Kirk James F. Davis** - Year:
**2001** - Publisher:
**American Mathematical Society** - Language:
**English** - ISBN:
**0-8218-2160-1,9780821821602,39-2001-514-2**

- DPI:
**600** - File size:
**3 358 930** - Format:
**djvu**

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Algebraic topology is the study of the global properties of spaces by means of algebra. It is an important branch of modern mathematics with a wide degree of applicability to other fields, including geometric topology, differential geometry, functional an...

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 understandi...

William S. Massey Professor Massey, born in Illinois in 1920, received his bachelor's degree from the University of Chicago and then served for four years in the U.S. Navy during World War II. After the War he received his Ph.D. from Princeton University ...

The articles in this volume study various cohomological aspects of algebraic varieties:- characteristic classes of singular varieties;- geometry of flag varieties;- cohomological computations for homogeneous spaces;- K-theory of algebraic varieties;- quan...

This textbook is intended for a course in algebraic topology at the beginning graduate level. The main topics covered are: the classification of compact 2-manifolds, the fundamental group, covering spaces, singular homology theory, and singular cohomology...

These lecture notes build upon a course Evans taught at the University of Maryland during the fall of 1983....

To the Teacher. This book is designed to introduce a student to some of the important ideas of algebraic topology by emphasizing the reÂ lations of these ideas with other areas of mathematics. Rather than choosing one point of view of modem topology (homo...

This is a charming book on algebraic topology.It doesnt teach homology or cohomology theory,still you can find in it:about the fundamental group, the action of the fundamental group on the universal cover (and the concept of the universal cover),the class...

Public Health Policy and Ethics brings together philosophers and practitioners to address the foundations and principles upon which public health policy may be advancedâ€”especially in the international arena. What is the basis that justifies public health ...

The goals and content for this book are derived from three important and ongoing efforts: to advance the institution of education and to promote educational opportunities to children and youth worldwide, to promote effective assessment policies and practi...

International Weather Radar Networking covers all aspects of the subject in a collection of contributions drawn from all over the world. Of particular interest are the papers describing work in Eastern Europe and papers reviewing of the achievements of th...

For decades retroviruses have been riding the crest of a wave of experimental research directed toward the identification of an infectious agent of human neoplastic diseases. In the early 1970s, several scientists successfully demonstrated the presence of...

Teacher research is recognized, in ELT and education more generally, as a powerful transformative strategy for teacher development and school improvement. This volume provides original insights into this issue by focusing on the processes involved in beco...

The central claim developed in this book is that disciplinary International Relations (IR) is identifiable as both an advanced colonial practice and a postcolonial subject. The starting problematic here issues from disciplinary IR's relative dearth of att...