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Lectures on Algebraic Topology

  • Albrecht Dold

Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 200)

Table of contents

  1. Front Matter
    Pages I-XI
  2. Albrecht Dold
    Pages 16-28
  3. Albrecht Dold
    Pages 29-53
  4. Albrecht Dold
    Pages 54-84
  5. Albrecht Dold
    Pages 123-185
  6. Albrecht Dold
    Pages 186-246
  7. Albrecht Dold
    Pages 247-367
  8. Back Matter
    Pages 368-380

About this book

Introduction

This is essentially a book on singular homology and cohomology with special emphasis on products and manifolds. It does not treat homotopy theory except for some basic notions, some examples, and some applica­ tions of (co-)homology to homotopy. Nor does it deal with general(-ised) homology, but many formulations and arguments on singular homology are so chosen that they also apply to general homology. Because of these absences I have also omitted spectral sequences, their main applications in topology being to homotopy and general (co-)homology theory. Cech­ cohomology is treated in a simple ad hoc fashion for locally compact subsets of manifolds; a short systematic treatment for arbitrary spaces, emphasizing the universal property of the Cech-procedure, is contained in an appendix. The book grew out of a one-year's course on algebraic topology, and it can serve as a text for such a course. For a shorter basic course, say of half a year, one might use chapters II, III, IV (§§ 1-4), V (§§ 1-5, 7, 8), VI (§§ 3, 7, 9, 11, 12). As prerequisites the student should know the elementary parts of general topology, abelian group theory, and the language of categories - although our chapter I provides a little help with the latter two. For pedagogical reasons, I have treated integral homology only up to chapter VI; if a reader or teacher prefers to have general coefficients from the beginning he needs to make only minor adaptions.

Keywords

Algebraic Algebraic topology Homotopy Topology cohomology group theory homology homotopy theory

Authors and affiliations

  • Albrecht Dold
    • 1
  1. 1.Mathematisches InstitutUniversität HeidelbergDeutschland

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-00756-3
  • Copyright Information Springer-Verlag Berlin Heidelberg 1972
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-662-00758-7
  • Online ISBN 978-3-662-00756-3
  • Series Print ISSN 0072-7830
  • Buy this book on publisher's site