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  • Algebraic Methods in Unstable Homotopy Theory by Joseph Neisendorfer (English) H

    • Item No : 146485619574
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      Algebraic Methods in Unstable Homotopy Theory

      by Joseph Neisendorfer

      The most modern and thorough treatment of unstable homotopy theory available. The focus is on those methods from algebraic topology which underlie the work of Cohen, Moore, and the author. Suitable for a course in unstable homotopy theory, it is also a valuable reference for experts and graduate students alike.

      FORMAT
      Hardcover
      LANGUAGE
      English
      CONDITION
      Brand New


      Publisher Description

      The most modern and thorough treatment of unstable homotopy theory available. The focus is on those methods from algebraic topology which are needed in the presentation of results, proven by Cohen, Moore, and the author, on the exponents of homotopy groups. The author introduces various aspects of unstable homotopy theory, including: homotopy groups with coefficients; localization and completion; the Hopf invariants of Hilton, James, and Toda; Samelson products; homotopy Bockstein spectral sequences; graded Lie algebras; differential homological algebra; and the exponent theorems concerning the homotopy groups of spheres and Moore spaces. This book is suitable for a course in unstable homotopy theory, following a first course in homotopy theory. It is also a valuable reference for both experts and graduate students wishing to enter the field.

      Author Biography

      Joseph Neisendorfer is Professor Emeritus in the Department of Mathematics at the University of Rochester, New York.

      Table of Contents

      Preface; Introduction; 1. Homotopy groups with coefficients; 2. A general theory of localization; 3. Fibre extensions of squares and the Peterson-Stein formula; 4. Hilton-Hopf invariants and the EHP sequence; 5. James-Hopf invariants and Toda-Hopf invariants; 6. Samelson products; 7. Bockstein spectral sequences; 8. Lie algebras and universal enveloping algebras; 9. Applications of graded Lie algebras; 10. Differential homological algebra; 11. Odd primary exponent theorems; 12. Differential homological algebra of classifying spaces; Bibliography; Index.

      Review

      'It is very well written and organized, as would be expected of the author, who is renowned for an excellent expository style ... the book could, and should, be used as a text for students aiming to do research in unstable homotopy theory. By the end of a thorough reading, a student would be well grounded in a suite of contemporary methods and would be ready to tackle research problems. the book's comprehensive nature also means that it is a wonderful reference for expects in the area.' Bulletin of the London Mathematical Society '... provides a new generation of topologists with a readable and workmanlike collection of important techniques and results ...' Mathematical Reviews "It is very well written and organized, as would be expected of the author, who is renowned for an excellent expository style. The book could, and should, be used as a text for students aiming to do research in unstable homotopy theory. By the end of a thorough reading, a student would be well grounded in a suite of contemporary methods and would be ready to tackle research problems. The book's comprehensive nature also means that it is a wonderful reference for experts in the area. In conclusion, this is a very good book and anyone in the field ought to have it near to hand."
      Stephen Theriault, Bulletin of the London Mathematical Society "... provides a new generation of topologists with a readable and workmanlike collection of important techniques and results, arranged in a readable sequence, with many interesting applications (not available anywhere else in a single source) treated in a unified manner."
      David A. Blanc, Mathematical Reviews

      Review Quote

      'It is very well written and organized, as would be expected of the author, who is renowned for an excellent expository style … the book could, and should, be used as a text for students aiming to do research in unstable homotopy theory. By the end of a thorough reading, a student would be well grounded in a suite of contemporary methods and would be ready to tackle research problems. the book's comprehensive nature also means that it is a wonderful reference for expects in the area.' Bulletin of the London Mathematical Society

      Promotional "Headline"

      The most modern and thorough treatment of unstable homotopy theory available.

      Description for Bookstore

      The most modern and thorough treatment of unstable homotopy theory available. The focus is on those methods from algebraic topology which underlie the work of Cohen, Moore, and the author. Suitable for a course in unstable homotopy theory, it is also a valuable reference for experts and graduate students alike.

      Description for Library

      The most modern and thorough treatment of unstable homotopy theory available. The focus is on those methods from algebraic topology which underlie the work of Cohen, Moore, and the author. Suitable for a course in unstable homotopy theory, it is also a valuable reference for experts and graduate students alike.

      Details

      ISBN0521760372
      Author Joseph Neisendorfer
      Short Title ALGEBRAIC METHODS IN UNSTABLE
      Publisher Cambridge University Press
      Series New Mathematical Monographs
      Language English
      ISBN-10 0521760372
      ISBN-13 9780521760379
      Media Book
      Format Hardcover
      Series Number 12
      DEWEY 514.24
      Imprint Cambridge University Press
      Place of Publication Cambridge
      Country of Publication United Kingdom
      Pages 554
      Year 2010
      Publication Date 2010-02-18
      Birth 1945
      Affiliation University of Rochester, New York
      Illustrations Worked examples or Exercises
      Audience Professional and Scholarly
      UK Release Date 2010-02-18
      AU Release Date 2010-02-18
      NZ Release Date 2010-02-18

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