Timeline for Generating cycles inside Tits' graph of words for a positive braid
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Feb 23 at 14:43 | review | Close votes | |||
| Feb 28 at 3:02 | |||||
| Feb 18 at 20:22 | comment | added | David E Speyer | I believe that I have proved it, using the extremely helpful reference @SamHopkins found. I wrote up the proof on my version of the question. | |
| Feb 17 at 22:53 | comment | added | David E Speyer | Allen, did you ever make progress on this? I just asked the same question mathoverflow.net/questions/464368 . | |
| Oct 9, 2022 at 16:46 | comment | added | Allen Knutson | Yeah, nonreducedness is important for me. I'm checking out the Guba-Sapir article math.vanderbilt.edu/sapirmv/ftp/pub/diagramgroups/dg.pdf | |
| Oct 9, 2022 at 16:17 | comment | added | Sam Hopkins | According to ams.org/journals/tran/2013-365-05/S0002-9947-2012-05719-9/…: "Tits [31] gave explicit generators for [the graph of reduced words's] fundamental group" and [31] is "J.A. Tits, A local approach to buildings. The geometric vein, pp. 519–547, Springer, New York–Berlin, 1981." This only answers your question in a special case but it might be a place to start for a reference. | |
| Oct 9, 2022 at 16:15 | comment | added | Carl-Fredrik Nyberg Brodda | You are really considering the braid semigroup $BS_n$, and (more generally, for any semigroup) your graphs are called the Squier complexes of the semigroup. The fundamental group of such a complex is called a diagram group, see e.g. Guba-Sapir. | |
| Oct 9, 2022 at 16:13 | comment | added | Sam Hopkins | Unless I'm getting confused about what you're asking, I think this is usually just called the "graph of reduced words" for an element of a Coxeter group (and you don't really need the language of braids to talk about it). EDIT: whoops, of course I am confused, because you are not necessarily considering reduced words. Sorry! I will leave this comment in case anyone makes the same mistake. | |
| Oct 9, 2022 at 15:51 | history | asked | Allen Knutson | CC BY-SA 4.0 |