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1. CMB 2017 (vol 60 pp. 604)

Louder, Larsen; Wilton, Henry
 Stackings and the $W$-cycles Conjecture 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 finitely generated Schur multiplier. Keywords:free groups, one-relator groups, right-orderabilityCategory:20F65

2. CMB 2012 (vol 56 pp. 881)

Xie, BaoHua; Wang, JieYan; Jiang, YuePing
 Free Groups Generated by Two Heisenberg Translations In this paper, we will discuss the groups generated by two Heisenberg translations of $\mathbf{PU}(2,1)$ and determine when they are free. Keywords:free group, Heisenberg group, complex triangle groupCategories:30F40, 22E40, 20H10
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