Talk:John R. Stallings

Bio details
I looked through the 1970 volume of the "Notices of AMS" hoping to find some more detailed bio info for Stallings, since he received the Cole Prize that year, but, unfortunately, they do not seem to have any relevant info available. There is a mention of the Cole prize being awarded in the program of the AMS annual meeting at San Antonio in Jan 1970 but no more details (I guess the names of the winners had not been announced before the meeting), and I did not find any follow-up info in the subsequent issues of the Notices. How annoying. I looked up the 1980 volume of the Notices (at that time the Cole Prize was awarded every five years; the 8-th was in 1970, the 9-th in 1975 and the 10th in 1980) and there they already give a detailed biographical sketch for the Cole Prize winners. If someone knows of any other source that can be used for verifying basic bio details such as the year of birth (which appears to be 1935 since the 65th birthday conference was in 2000), please chime in. Nsk92 (talk) 14:49, 6 August 2008 (UTC)
 * By the way, thanks very much for your work on the article. It is much improved and in a good state.  I think biographical articles can serve as great surveys of fields, and you've introduced a nice range of topics in this article. JackSchmidt (talk) 15:02, 6 August 2008 (UTC)

Stalling's theorem - please explain
There is something I don't understand about Stalling's characterization of the finitely generated groups that have more than one end. The statement implies that $$\mathbb Z$$ can be split as a nontrivial amagamated free product or an HNN extension. Can you describe such a decomposition? (I don't see how one could be possible). Oded (talk) 15:39, 11 August 2008 (UTC)
 * Yes, sure. The group $$\mathbb Z$$ is an HNN-extension of the trivial group with both associated subgroups trivial as well. You can write its HNN-presentation as $$\langle t | t^{-1}1t=1\rangle.$$ In the graph-of-groups language, this HNN-extension presentation of $$\mathbb Z$$ is the fundamental group of the graph of groups consisting of a single vertex a single loop-edge, where the vertex group and the edge group are trivial. Similarly, a free group of arbitrary rank is a multiple HNN-extension of the trivial group where the stable letters are the free generators. Nsk92 (talk) 15:46, 11 August 2008 (UTC)
 * Thanks. I thought the word nontrivial in the statement applied to both the splitting and the HNN representations. But from what you are saying, the HNN presentation can be trivial. If that's correct, perhaps it is better to clarify by writing instead "admits a splitting as an HNN-extension over a finite group or as a nontrivial amalgamated free product"? Oded (talk) 16:28, 11 August 2008 (UTC)
 * Yes, probably some clarification is needed here. I was using the word "nontrivial splitting" here in the sense it is usually used in Bass-Serre theory: when the action on the Bass-Serre covering tree does not have a global fixed point for the group (this definition is actually explained in the article Bass-Serre theory). In that sense, an HNN-extension splitting is always nontrivial and an amalgamated free product splitting is nontrivial exactly when the amalgamated subgroup has index > 1 in each of the factors. But you are right, probably a more explicit clarification is in order here. Nsk92 (talk) 17:10, 11 August 2008 (UTC)
 * OK, I have added an explicit stetement of the theorem to the article. It is probably better to create a separate article for Stallings theorem about ends of groups and to move such an explicit statement there, but it'll take me a while to get to it. Nsk92 (talk) 17:30, 11 August 2008 (UTC)

Assessment comment
Substituted at 20:20, 29 April 2016 (UTC)

External links modified
Hello fellow Wikipedians,

I have just modified 4 external links on John R. Stallings. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
 * Added archive https://web.archive.org/web/20080906110731/http://atlas-conferences.com/cgi-bin/calendar/d/faam71 to http://atlas-conferences.com/cgi-bin/calendar/d/faam71
 * Added archive https://web.archive.org/web/20080705172541/http://www.mrlonline.org/mrl/2007-014-004/2007-014-004-001.pdf to http://www.mrlonline.org/mrl/2007-014-004/2007-014-004-001.pdf
 * Added archive https://web.archive.org/web/20070715035528/http://nyjm.albany.edu:8000/PacJ/p/2000/196-2-13.pdf to http://nyjm.albany.edu:8000/PacJ/p/2000/196-2-13.pdf
 * Added archive https://web.archive.org/web/20080808135028/http://www.math.berkeley.edu/~stall to http://math.berkeley.edu/~stall/

When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.

Cheers.— InternetArchiveBot  (Report bug) 18:52, 25 April 2017 (UTC)

External links modified
Hello fellow Wikipedians,

I have just modified one external link on John R. Stallings. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
 * Added archive https://web.archive.org/web/20081228075259/http://math.berkeley.edu/home.html to http://math.berkeley.edu/home.html

When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.

Cheers.— InternetArchiveBot  (Report bug) 18:14, 28 November 2017 (UTC)