Timeline for Frohman & Fine's proof about Bianchi groups as HNN extensions (or anyone else's)
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 3, 2014 at 0:40 | vote | accept | j0equ1nn | ||
| Jan 3, 2014 at 0:39 | answer | added | j0equ1nn | timeline score: 0 | |
| Jan 3, 2014 at 0:37 | comment | added | j0equ1nn | This is in fact covered by the 2nd reference I listed. I'm going to post that as an answer to this question now. | |
| Dec 31, 2013 at 0:26 | comment | added | j0equ1nn | By the way, for the sake of motivating this conversation, there's a conjecture by Walter Neumann that for every algebraic number field, there is a hyperbolic 3-manifold having it as its invariant trace field. The Frohman/Fine result I'm searching for is an important ingredient in constructing manifolds having concatenations of quadratic extensions as their trace fields, and it can then be shown that all fields like that are possible as invariant trace fields (though the full conjecture is as of yet unresolved). | |
| Dec 30, 2013 at 22:54 | comment | added | j0equ1nn | @DanPetersen Okay, thanks very much for the advice. It look like I should read the 2nd article I listed more carefully once I have time and see if that resolves it (I have some other material I need to prepare for upcoming talks). If that doesn't work I'll try asking the authors. | |
| Dec 30, 2013 at 20:43 | comment | added | Dan Petersen | Finally, If you can't figure out what's going on then I suggest you send them an e-mail! | |
| Dec 30, 2013 at 20:43 | comment | added | Dan Petersen | @j0equ1nn No, I would not expect the CR article to include a reference to an expected full version. Without having read either paper, I think that most likely the proofs of the results announced in the CR note are exactly what is in the second article you referenced. If there is a discrepancy between what's stated in the two papers, then my guess is that either they thought of the result as an easy corollary and forgot to state it explicitly in the Proc. AMS paper, or that they found a gap in their argument when they worked out the details, and in the end stated only a weaker version. | |
| Dec 30, 2013 at 11:05 | comment | added | j0equ1nn | Anybody know if this proof is done in Fine's book Algebraic Theory of the Bianchi Groups (1989)? It looks kind of rare but I could probably buy it online somewhere. | |
| Dec 30, 2013 at 10:55 | comment | added | j0equ1nn | Ah yes, I was confused about which journal to be looking for. The reference I was following just had the abbreviation "Comp. Rend. R.S.C. Math." Now I see RSC is for Royal Society of Canada. I will see if I can get my hands on that next time I'm at school, but also as @DanPetersen mentioned, that may not help! Would you expect the journal to indicate where the full version was expected to be published? | |
| Dec 29, 2013 at 10:40 | comment | added | Dan Petersen | Also, most likely the Comptes Rendus note will not contain a proof of the result you want. CR is a journal for short and rapid announcements of results for which complete proofs will appear later elsewhere. | |
| Dec 29, 2013 at 10:34 | comment | added | Dan Petersen | @AndyPutman Probably you're thinking of the French journal, Comptes Rendus Mathematique - but the article he mentions is in the similarly named Canadian journal, mr.math.ca | |
| Dec 29, 2013 at 6:08 | comment | added | Andy Putman | (maybe the issue is that like in your question above you spelled the journal name wrong? it can be difficult to track down foreign-language journals in some libraries, especially ones like CR which have undergone huge numbers of name changes over the years. that's why I suggest talking to a librarian.) | |
| Dec 29, 2013 at 6:01 | comment | added | Andy Putman | Your profile says that you're at CUNY right now. I would be very surprised if the CUNY library did not have back issues of Comptes Rendus; it's a very well-known journal. Ask your librarian (they can probably get it via interlibrary loan if necessary). Another option would be to check out Columbia's library, which certainly will have it. | |
| Dec 29, 2013 at 5:58 | history | edited | j0equ1nn | CC BY-SA 3.0 |
added missing ); added 2 characters in body
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| Dec 29, 2013 at 0:10 | history | asked | j0equ1nn | CC BY-SA 3.0 |