Geodesic
Stackings and the W-cycles Conjecture
Canadian mathematical bulletin, Tome 60 (2017) no. 3, pp. 604-612

Voir la notice de l'article provenant de la source Cambridge University Press

We prove Wise's $W$ -cycles conjecture. Consider a compact graph $\Gamma '$ immersing into another graph $\Gamma $ . For any immersed cycle $\Lambda :{{S}^{1}}\to \Gamma $ , we consider the map $\Lambda '$ from the circular components $\mathbb{S}$ of the pullback to $\Gamma '$ . Unless $\Lambda '$ is reducible, the degree of the covering map $\mathbb{S}\to {{S}^{1}}$ is bounded above by minus the Euler characteristic of $\Gamma '$ . As a corollary, any finitely generated subgroup of a one-relator group has a finitely generated Schur multiplier.
DOI : 10.4153/CMB-2016-078-3
Mots-clés : 20F65, free groups, one-relator groups, right-orderability 
Louder, Larsen; Wilton, Henry. Stackings and the W-cycles Conjecture. Canadian mathematical bulletin, Tome 60 (2017) no. 3, pp. 604-612. doi: 10.4153/CMB-2016-078-3
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[Bau74] [Bau74] Baumslag, G., Some problems on one-relator groups. In: Proceedings of the Second International Conference on the Theory of Groups (Australian Nat. Univ., Canberra, 1973), Lecture Notes in Math., 372, Springer, Berlin, 1974, pp. 75–81. Google Scholar

[Bro80] [Bro80] Brodskii, S. D., Equations over groups and groups with one defining relation. Uspekhi Mat. Nauk 35(1980), no. 4(214), 183. Google Scholar

[DH91] [DH91] Duncan, A. J. and J. Howie, The genus problem for one-relator products of locally indicable Google Scholar

groups. Math. Z. 208(1991), no. 2, 225–237. http://dx.doi.Org/10.1007/BF02571522 Google Scholar

[Far76] [Far76] Farrell, E. T., Right-orderable deck transformation groups. Rocky Mountain J. Math. 6(1976), no. 3, 441–447. http://dx.doi.Org/10.1216/RMJ-1976-6-3-441 Google Scholar

[HW16] [HW16] Heifer, J. and Wise, D. T., Counting cycles in labeled graphs: the nonpositive immersions property for one-relator groups. Int. Math. Res. Not. IMRN 2016, no. 9, 2813–2827. http://dx.doi.Org/10.1093/imrn/mv208 Google Scholar

[How81] [How81] Howie, J., On pairs of 2-complexes and systems of equations over groups. J. Reine Angew. Math. 324(1981), 165–174. http://dx.doi.Org/10.1 51 5/crll.1 981.324.1 65 Google Scholar

[How82] [How82] , On locally indicable groups. Math. Z. 180(1982), no. 4, 445–461. http://dx.doi.Org/10.1007/BF01 21471 7 Google Scholar

[Lyn50] [Lyn50] Lyndon, R. C., Cohomology theory of groups with a single defining relation. Ann. of Math. (2) 52(1950), 650–665. http://dx.doi.Org/10.2307/1 969440 Google Scholar

[Sco73] [Sco73] Scott, G. P., Finitely generated 3-manifold groups are finitely presented. J. London Math. Soc. (2) 6(1973), 437–440. http://dx.doi.Org/10.1112/jlms/s2-6.3.437 Google Scholar

[Sta83] [Sta83] Stallings, J. R., Topology of finite graphs. Invent. Math. 71(1983), no. 3, 551–565. http://dx.doi.Org/10.1007/BF02095993 Google Scholar

[WisO5] [WisO5] Wise, D. T., The coherence of one-relator groups with torsion and the Hanna Neumann conjecture. Bull. London Math. Soc. 37(2005), no. 5, 697–705. http://dx.doi.Org/!0.1112/S0024609305004376 Google Scholar

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