IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-1-4684-9322-1_8.html
   My bibliography  Save this book chapter

Homotopy Theory

In: Algebraic Topology

Author

Listed:
  • Edwin H. Spanier

    (University of California, Department of Mathematics)

Abstract

with this chapter we return to the consideration of general homotopy theory. Now that we have homology theory available as a tool, we are able to obtain deeper results about homotopy than we could without it. We shall consider the higher homotopy groups in some detail and prove they satisfy analogues of all the axioms of homology theory except the excision axiom. We introduce the Hurewicz homomorphism as a natural transformation from the homotopy groups to the integral singular homology groups. It leads us to the Hurewicz isomorphism theorem, which states roughly that the lowest-dimensional nontrivial homotopy group is isomorphic to the corresponding integral homology group.

Suggested Citation

  • Edwin H. Spanier, 1966. "Homotopy Theory," Springer Books, in: Algebraic Topology, chapter 0, pages 362-421, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4684-9322-1_8
    DOI: 10.1007/978-1-4684-9322-1_8
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-1-4684-9322-1_8. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.