Journal article
Poorly connected groups
- Abstract:
- We investigate groups whose Cayley graphs have poorly connected subgraphs. We prove that a finitely generated group has bounded separation in the sense of Benjamini-Schramm-Timár if and only if it is virtually free. We then prove a gap theorem for connectivity of finitely presented groups, and prove that there is no comparable theorem for all finitely generated groups. Finally, we formulate a connectivity version of the conjecture that every group of type F with no Baumslag-Solitar subgroup is hyperbolic, and prove it for groups with at most quadratic Dehn function.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
Actions
Access Document
- Files:
-
-
(Preview, Accepted manuscript, pdf, 196.3KB, Terms of use)
-
- Publisher copy:
- 10.1090/proc/15128
Authors
- Publisher:
- American Mathematical Society
- Journal:
- Proceedings of the American Mathematical Society More from this journal
- Volume:
- 148
- Issue:
- 2020
- Pages:
- 4653-4664
- Publication date:
- 2020-08-14
- Acceptance date:
- 2020-04-13
- DOI:
- EISSN:
-
1088-6826
- ISSN:
-
0002-9939
- Language:
-
English
- Keywords:
- Pubs id:
-
991889
- Local pid:
-
pubs:991889
- Deposit date:
-
2020-05-01
- ARK identifier:
Terms of use
- Copyright holder:
- Hume and MacKay
- Copyright date:
- 2020
- Rights statement:
- © 2020 Copyright by the authors
- Notes:
- This is the accepted manuscript version of the article. The final version is available online from American Mathematical Society at https://doi.org/10.1090/proc/15128
If you are the owner of this record, you can report an update to it here: Report update to this record