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Homotopical Topology

  • Anatoly Fomenko
  • Dmitry Fuchs

Part of the Graduate Texts in Mathematics book series (GTM, volume 273)

Table of contents

  1. Front Matter
    Pages i-xxxv
  2. Anatoly Fomenko, Dmitry Fuchs
    Pages 25-142
  3. Anatoly Fomenko, Dmitry Fuchs
    Pages 143-303
  4. Anatoly Fomenko, Dmitry Fuchs
    Pages 305-387
  5. Anatoly Fomenko, Dmitry Fuchs
    Pages 389-428
  6. Anatoly Fomenko, Dmitry Fuchs
    Pages 429-494
  7. Anatoly Fomenko, Dmitry Fuchs
    Pages 495-611
  8. Back Matter
    Pages 613-627

About this book

Introduction

This classic text of the renowned Moscow mathematical school equips the aspiring mathematician with a solid grounding in the core of topology, from a homotopical perspective. Its comprehensiveness and depth of treatment are unmatched among topology textbooks: in addition to covering the basics—the fundamental notions and constructions of homotopy theory, covering spaces and the fundamental group, CW complexes, homology and cohomology, homological algebra—the book treats essential advanced topics, such as obstruction theory, characteristic classes, Steenrod squares, K-theory and cobordism theory, and, with distinctive thoroughness and lucidity, spectral sequences. The organization of the material around the major achievements of the golden era of topology—the Adams conjecture, Bott periodicity, the Hirzebruch–Riemann–Roch theorem, the Atiyah–Singer index theorem, to name a few—paints a clear picture of the canon of the subject. Grassmannians, loop spaces, and classical groups play a central role in mathematics, and therefore in the presentation of this book, as well.

A judicious focus on the key ideas, at an appropriate magnification of detail, enables the reader to navigate the breadth of material, confidently, without the disorientation of algebraic minutiae. Many exercises are integrated throughout the text to build up the reader’s mastery of concepts and techniques. Numerous technical illustrations elucidate geometric constructions and the mechanics of spectral sequences and other sophisticated methods. Over fifty hauntingly captivating images by A. T. Fomenko artistically render the wondrous beauty, and mystery, of the subject.

Keywords

CW complexes K-theory Riemann-Roch theorem algebraic topology cohomology fundamental group homology spectral sequences

Authors and affiliations

  • Anatoly Fomenko
    • 1
  • Dmitry Fuchs
    • 2
  1. 1.Dept of Math & MechanicsMoscow State UniversityMoscowRussia
  2. 2.Department of MathematicsUniversity of CaliforniaDavisUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-23488-5
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-23487-8
  • Online ISBN 978-3-319-23488-5
  • Series Print ISSN 0072-5285
  • Series Online ISSN 2197-5612
  • Buy this book on publisher's site