Journal article
Residually finite rationally solvable groups and virtual fibring
- Abstract:
- We show that a finitely generated residually finite rationally solvable (or RFRS) group $G$ is virtually fibred, in the sense that it admits a virtual surjection to $\mathbb{Z}$ with a finitely generated kernel, if and only if the first $L^2$-Betti number of $G$ vanishes. This generalises (and gives a new proof of) the analogous result of Ian Agol for fundamental groups of $3$-manifolds.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
Actions
Access Document
- Files:
-
-
(Preview, Accepted manuscript, 398.2KB, Terms of use)
-
- Publisher copy:
- 10.1090/jams/936
Authors
- Publisher:
- American Mathematical Society
- Journal:
- Journal of the American Mathematical Society More from this journal
- Volume:
- 33
- Issue:
- 2
- Pages:
- 451-486
- Publication date:
- 2019-12-24
- DOI:
- EISSN:
-
1088-6834
- ISSN:
-
0894-0347
Terms of use
- Copyright holder:
- American Mathematical Society
- Copyright date:
- 2019
- Rights statement:
- © Copyright 2019 American Mathematical Society
- Notes:
- This is the accepted manuscript version of the article. The final version is available from American Mathematical Society at: https://doi.org/10.1090/jams/936
If you are the owner of this record, you can report an update to it here: Report update to this record