Topology I

General Survey

  • S. P. Novikov

Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 12)

Table of contents

  1. Front Matter
    Pages i-v
  2. Sergei P. Novikov
    Pages 1-319
  3. Back Matter
    Pages 321-322

About this book

Introduction

This book constitutes nothing less than an up-to-date survey of the whole field of topology (with the exception of "general (set-theoretic) topology"), or, in the words of Novikov himself, of what was termed at the end of the 19th century "Analysis Situs", and subsequently diversified into the various subfields of combinatorial, algebraic, differential, homotopic, and geometric topology. The book gives an overview of these subfields, beginning with the elements and proceeding right up to the present frontiers of research. Thus one finds here the whole range of topological concepts from fibre spaces (Chap.2), CW-complexes, homology and homotopy, through bordism theory and K-theory to the Adams-Novikov spectral sequence (Chap.3), and in Chapter 4 an exhaustive (but necessarily concentrated) survey of the theory of manifolds. An appendix sketching the recent impressive developments in the theory of knots and links and low-dimensional topology generally, brings the survey right up to the present. This work represents the flagship, as it were, in whose wake follow more detailed surveys of the various subfields, by various authors.

Keywords

Algebraic Topology Algebraische Topologie Homotopy K-theory Topological Methods in Geometry Topologie Topologie der Mannigfaltigkeiten Topologie, Geometrische Topology Topology of Manifolds homology manifold

Editors and affiliations

  • S. P. Novikov
    • 1
    • 2
  1. 1.Institute for Physical Science and TechnologyUniversity of MarylandCollege ParkUSA
  2. 2.Landau Institute for Theoretical Physics of the Russian Academy of SciencesMoscowRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-10579-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 1996
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-05735-9
  • Online ISBN 978-3-662-10579-5
  • Series Print ISSN 0938-0396
  • About this book