Timeline for Free splittings of one-relator groups
Current License: CC BY-SA 2.5
3 events
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| Jun 1, 2010 at 15:59 | comment | added | HJRW | Regarding your second paragraph: from the Bass--Serre Theory point of view, we're really talking about actions on trees with trivial edge stabilizers; this boils down to free products or HNN extensions over the trivial group. A group G is an HNN extension over the trivial group if and only if it's a non-trivial free product with a $\mathbb{Z}$ factor or $G\cong\mathbb{Z}$. In my remark, I wanted to give a 'natural' reason why $\mathbb{Z}$ wasn't a counterexample, without mentioning actions on trees. I don't think there's anything natural about excluding something by fiat. | |
| Jun 1, 2010 at 15:54 | comment | added | HJRW | Thanks for the answer Tom. Yes, I know about the Freiheitssatz; I don't see how it helps with this question directly. It's certainly conceivable that the Magnus-rewriting-and-induction proof scheme of the Freiheittsatz could be applied to prove what I want. Unfortunately, I don't have a strong enough feeling for that method to know what's possible and what's not. | |
| Jun 1, 2010 at 5:49 | history | answered | Tom Church | CC BY-SA 2.5 |