Louder, L;
Wilton, H;
(2017)
Stackings and the W-cycles Conjecture.
Canadian Mathematical Bulletin
, 60
pp. 604-612.
10.4153/CMB-2016-078-3.
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Abstract
We prove Wise’s W-cycles conjecture: Consider a compact graph Γ0 immersing into another graph Γ. For any immersed cycle Λ : S1 → Γ, we consider the map Λ0 from the circular components S of the pullback to Γ0. Unless Λ0 is reducible, the degree of the covering map S → S1 is bounded above by minus the Euler characteristic of Γ0. As a corollary, any finitely generated subgroup of a one-relator group has finitely generated Schur multiplier.
| Type: | Article |
|---|---|
| Title: | Stackings and the W-cycles Conjecture |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.4153/CMB-2016-078-3 |
| Publisher version: | http://dx.doi.org/10.4153/CMB-2016-078-3 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Free groups, one-relator groups, right-orderability |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1493364 |
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