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Softcover ISBN:  9780821844366 
Product Code:  FIM/9.S 
List Price:  $68.00 
MAA Member Price:  $61.20 
AMS Member Price:  $54.40 
eBook ISBN:  9781470431365 
Product Code:  FIM/9.E 
List Price:  $63.00 
MAA Member Price:  $56.70 
AMS Member Price:  $50.40 
Softcover ISBN:  9780821844366 
eBook ISBN:  9781470431365 
Product Code:  FIM/9.S.B 
List Price:  $131.00 $99.50 
MAA Member Price:  $117.90 $89.55 
AMS Member Price:  $104.80 $79.60 

Book DetailsFields Institute MonographsVolume: 9; 1997; 188 ppMSC: Primary 55; Secondary 18; 54; 57
This text is based on a onesemester graduate course taught by the author at The Fields Institute in fall 1995 as part of the homotopy theory program which constituted the Institute's major program that year. The intent of the course was to bring graduate students who had completed a first course in algebraic topology to the point where they could understand research lectures in homotopy theory and to prepare them for the other, more specialized graduate courses being held in conjunction with the program. The notes are divided into two parts: prerequisites and the course proper.
Part I, the prerequisites, contains a review of material often taught in a first course in algebraic topology. It should provide a useful summary for students and nonspecialists who are interested in learning the basics of algebraic topology. Included are some basic category theory, point set topology, the fundamental group, homological algebra, singular and cellular homology, and Poincaré duality.
Part II covers fibrations and cofibrations, Hurewicz and cellular approximation theorems, topics in classical homotopy theory, simplicial sets, fiber bundles, Hopf algebras, spectral sequences, localization, generalized homology, and cohomology operations.
This book collects in one place the material that a researcher in algebraic topology must know. The author has attempted to make this text a selfcontained exposition. Precise statements and proofs are given of “folk” theorems which are difficult to find or do not exist in the literature.
Titles in this series are copublished with The Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).
ReadershipGraduate students and research mathematicians interested in algebraic topology and mathematicians specializing in other areas who wish to learn the basics of algebraic topology or more advanced material in homotopy theory.

Table of Contents

Part I. Prerequisites

Chapter 1. Prerequisites from category theory

Chapter 2. Prerequisites from point set topology

Chapter 3. The fundamental group

Chapter 4. Homological algebra

Chapter 5. Homology of spaces

Chapter 6. Manifolds

Part II. Homotopy Theory

Chapter 7. Higher homotopy theory

Chapter 8. Simplicial sets

Chapter 9. Fibre bundles and classifying spaces

Chapter 10. Hopf algebras and graded Lie algebras

Chapter 11. Spectral sequences

Chapter 12. Localization and completion

Chapter 13. Generalized homology and stable homotopy

Chapter 14. Cohomology operations and the Steenrod algebra


Reviews

A comprehensive introduction to many topics in algebraic topology up to the tools currently used in research ... the author has pulled off a real tour de force ... could serve as an excellent route into some of the most exciting topics in mathematics.
Zentralblatt MATH 
Shows a wellmarked trail to homotopy theory with plenty of beautiful scenery worth visiting, while leaving to the student the task of hiking along it. Most of us wish we had had this book when we were students.
Mathematical Reviews


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This text is based on a onesemester graduate course taught by the author at The Fields Institute in fall 1995 as part of the homotopy theory program which constituted the Institute's major program that year. The intent of the course was to bring graduate students who had completed a first course in algebraic topology to the point where they could understand research lectures in homotopy theory and to prepare them for the other, more specialized graduate courses being held in conjunction with the program. The notes are divided into two parts: prerequisites and the course proper.
Part I, the prerequisites, contains a review of material often taught in a first course in algebraic topology. It should provide a useful summary for students and nonspecialists who are interested in learning the basics of algebraic topology. Included are some basic category theory, point set topology, the fundamental group, homological algebra, singular and cellular homology, and Poincaré duality.
Part II covers fibrations and cofibrations, Hurewicz and cellular approximation theorems, topics in classical homotopy theory, simplicial sets, fiber bundles, Hopf algebras, spectral sequences, localization, generalized homology, and cohomology operations.
This book collects in one place the material that a researcher in algebraic topology must know. The author has attempted to make this text a selfcontained exposition. Precise statements and proofs are given of “folk” theorems which are difficult to find or do not exist in the literature.
Titles in this series are copublished with The Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).
Graduate students and research mathematicians interested in algebraic topology and mathematicians specializing in other areas who wish to learn the basics of algebraic topology or more advanced material in homotopy theory.

Part I. Prerequisites

Chapter 1. Prerequisites from category theory

Chapter 2. Prerequisites from point set topology

Chapter 3. The fundamental group

Chapter 4. Homological algebra

Chapter 5. Homology of spaces

Chapter 6. Manifolds

Part II. Homotopy Theory

Chapter 7. Higher homotopy theory

Chapter 8. Simplicial sets

Chapter 9. Fibre bundles and classifying spaces

Chapter 10. Hopf algebras and graded Lie algebras

Chapter 11. Spectral sequences

Chapter 12. Localization and completion

Chapter 13. Generalized homology and stable homotopy

Chapter 14. Cohomology operations and the Steenrod algebra

A comprehensive introduction to many topics in algebraic topology up to the tools currently used in research ... the author has pulled off a real tour de force ... could serve as an excellent route into some of the most exciting topics in mathematics.
Zentralblatt MATH 
Shows a wellmarked trail to homotopy theory with plenty of beautiful scenery worth visiting, while leaving to the student the task of hiking along it. Most of us wish we had had this book when we were students.
Mathematical Reviews