Download this article
 Download this article For screen
For printing
Recent Issues

Volume 30
Issue 7, 2431–2778
Issue 6, 2043–2429
Issue 5, 1611–2042
Issue 4, 1203–1610
Issue 3, 835–1201
Issue 2, 389–833
Issue 1, 1–388

Volume 29, 9 issues

Volume 28, 9 issues

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
 
Author index
To appear
 
Other MSP journals
On the cohomological dimension of kernels of maps to $\mathbb{Z}$

Sam P. Fisher

Geometry & Topology 30 (2026) 373–388
Bibliography
1 I Agol, Criteria for virtual fibering, J. Topol. 1 (2008) 269 MR2399130
2 I Agol, M Stover, Congruence RFRS towers, Ann. Inst. Fourier (Grenoble) 73 (2023) 307 MR4588931
3 G Baumslag, A survey of groups with a single defining relation, from: "Proceedings of groups" (editors E F Robertson, C M Campbell), London Math. Soc. Lecture Note Ser. 121, Cambridge Univ. Press (1986) 30 MR896500
4 R Bieri, Homological dimension of discrete groups, Queen Mary College (1981) MR715779
5 R Bieri, B Renz, Valuations on free resolutions and higher geometric invariants of groups, Comment. Math. Helv. 63 (1988) 464 MR960770
6 W Dicks, P A Linnell, L2-Betti numbers of one-relator groups, Math. Ann. 337 (2007) 855 MR2285740
7 G Duchamp, D Krob, The lower central series of the free partially commutative group, Semigroup Forum 45 (1992) 385 MR1179860
8 G L Feldman, The homological dimension of group algebras of solvable groups, Izv. Akad. Nauk SSSR Ser. Mat. 35 (1971) 1225 MR296168
9 S P Fisher, Improved algebraic fibrings, Compos. Math. 160 (2024) 2203 MR4797112
10 S P Fisher, K Klinge, Dimension drop in residual chains, (2024) arXiv:2410.08153
11 S P Fisher, I Morales, The Hanna Neumann conjecture for graphs of free groups with cyclic edge groups, Compos. Math. 161 (2025) 1576 MR4958711
12 M Hagen, D T Wise, Special groups with an elementary hierarchy are virtually free-by-, Groups Geom. Dyn. 4 (2010) 597 MR2653976
13 F Haglund, D T Wise, Special cube complexes, Geom. Funct. Anal. 17 (2008) 1551 MR2377497
14 T Hsu, D T Wise, Cubulating graphs of free groups with cyclic edge groups, Amer. J. Math. 132 (2010) 1153 MR2732342
15 I Hughes, Division rings of fractions for group rings, Comm. Pure Appl. Math. 23 (1970) 181 MR263934
16 A Jaikin-Zapirain, The universality of Hughes-free division rings, Selecta Math. 27 (2021) 74 MR4292784
17 D Kielak, Residually finite rationally solvable groups and virtual fibring, J. Amer. Math. Soc. 33 (2020) 451 MR4073866
18 D Kielak, M Linton, Virtually free-by-cyclic groups, Geom. Funct. Anal. 34 (2024) 1580 MR4792841
19 D Kielak, R Kropholler, G Wilkes, 2-Betti numbers and coherence of random groups, J. Lond. Math. Soc. 106 (2022) 425 MR4454494
20 P A Linnell, Division rings and group von Neumann algebras, Forum Math. 5 (1993) 561 MR1242889
21 W Lück, L2-invariants : theory and applications to geometry and K-theory, 44, Springer (2002) MR1926649
22 B B Newman, Some results on one-relator groups, Bull. Amer. Math. Soc. 74 (1968) 568 MR222152
23 T Schick, Erratum : “Integrality of L2-Betti numbers”, Math. Ann. 322 (2002) 421 MR1894160
24 J C Sikorav, Homologie de Novikov associée à une classe de cohomologie de degré un, PhD thesis, Université Paris-Sud (1987)
25 J R Stallings, On torsion-free groups with infinitely many ends, Ann. of Math. 88 (1968) 312 MR228573
26 R G Swan, Groups of cohomological dimension one, J. Algebra 12 (1969) 585 MR240177
27 D T Wise, An invitation to coherent groups, from: "What’s next ? : the mathematical legacy of William P. Thurston" (editors D P Thurston, W P Thurston), Ann. of Math. Stud. 205, Princeton Univ. Press (2020) 326 MR4205645
28 D T Wise, A note on the vanishing of the 2nd L2-Betti number, Proc. Amer. Math. Soc. 148 (2020) 3239 MR4108834
29 D T Wise, The structure of groups with a quasiconvex hierarchy, 209, Princeton Univ. Press (2021) MR4298722
30 D T Wise, Coherence, local indicability and nonpositive immersions, J. Inst. Math. Jussieu 21 (2022) 659 MR4386825
31 D T Wise, Criteria for the vanishing of H2(2), Indiana Univ. Math. J. 71 (2022) 409 MR4395602