Timeline for Subgroups of one-relator groups
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Mar 15, 2021 at 20:20 | comment | added | Carl-Fredrik Nyberg Brodda | @HJRW Yes, of course you're right. Thanks for writing this out! In fact, an earlier version of Bob's paper on the arXiv did not have that argument, after which Howie wrote to him to provide exactly that argument. | |
| Mar 15, 2021 at 18:31 | comment | added | HJRW | Sorry for the extended comments. Looking at Gray's paper, I see that the non-embeddability result is in fact proved by appealing to out work, exactly as the above comments suggest! | |
| Mar 15, 2021 at 18:27 | comment | added | HJRW | (By the way, the point about RAAGs is just the observation that the Euler characteristic of a 2-dimenional RAAG defined by the graph $\Gamma$ is $1-\chi(\Gamma)$.) | |
| Mar 15, 2021 at 18:14 | comment | added | HJRW | ... For details, see arxiv.org/abs/1410.2540, arxiv.org/abs/1805.11976 and arxiv.org/abs/1410.2579 . Much stronger results, which apply to many but not all one-relator groups, are proved in arxiv.org/abs/1803.02671 . | |
| Mar 15, 2021 at 18:14 | comment | added | HJRW | I think most of these, and much more general, non-embeddability results can be extracted from recent work of Louder--myself, Helfer--Wise and Wise. In summary, we prove that every finitely generated, infinite subgroup of a one-relator group has Euler characteristic at most zero. For a freely indecomposable RAAG, it follows the underlying graph is a tree... | |
| Mar 15, 2021 at 13:34 | history | edited | Carl-Fredrik Nyberg Brodda | CC BY-SA 4.0 |
Fixed an important fact about subgroups of torsion.
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| Mar 15, 2021 at 11:40 | comment | added | Carl-Fredrik Nyberg Brodda | @YCor Yes, but this already follows from the fact that the cohomological dimension of any torsion-free one-relator group is $\leq 2$. | |
| Mar 15, 2021 at 11:29 | comment | added | YCor | The raag statement seems to include as particular case that $\mathbf{Z}^3$ doesn't embed into a 1-relator group. | |
| Mar 15, 2021 at 11:09 | history | answered | Carl-Fredrik Nyberg Brodda | CC BY-SA 4.0 |