IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-1-4612-4668-8_17.html

Appendix: The Dehn-Nielsen Theorem

In: Papers on Group Theory and Topology

Author

Listed:
  • John Stillwell

Abstract

One important theorem attributed to Dehn does not appear in his published work, and his proof of it seems to be lost. This is the theorem that every automorphism of the fundamental group πl (S) of a closed orientable surface S can be induced by a homeomorphism of S. The earliest known proof appears in Nielsen [1927], and consists of two parts. The first, which is in §9 of Nielsen’s paper and expounded below as Theorem 5, is quite elegant and is attributed to Dehn. The second, in §23, is agonisingly long and is apparently Nielsen’s own, though he still credited the theorem to Dehn. As was mentioned in the introduction to Paper 7, Nielsen in 1931 found a replacement for §23 which was much simpler, but he did not publish it. We give a similar proof below as Theorem 6.

Suggested Citation

  • John Stillwell, 1987. "Appendix: The Dehn-Nielsen Theorem," Springer Books, in: Papers on Group Theory and Topology, pages 363-396, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-4668-8_17
    DOI: 10.1007/978-1-4612-4668-8_17
    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:978-1-4612-4668-8_17. 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.