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
onerelator group has finitely generated Schur multiplier.
Keywords:free groups, onerelator groups, rightorderability Category:20F65 

2. CMB 2016 (vol 60 pp. 54)
 Button, Jack

Tubular Free by Cyclic Groups Act Freely on CAT(0) Cube Complexes
We identify when a tubular group (the fundamental group of a
finite
graph of groups with $\mathbb{Z}^2$ vertex and $\mathbb{Z}$ edge groups) is free
by
cyclic and show, using Wise's equitable sets criterion, that
every
tubular free by
cyclic group acts freely on a CAT(0) cube complex.
Keywords:CAT(0), tubular group Categories:20F65, 20F67, 20E08 

3. CMB 2016 (vol 60 pp. 77)
 Christ, Michael; Rieffel, Marc A.

Nilpotent Group C*algebras as Compact Quantum Metric Spaces
Let $\mathbb{L}$ be a length function on a group $G$, and let $M_\mathbb{L}$
denote the
operator of pointwise multiplication by $\mathbb{L}$ on $\lt(G)$.
Following Connes,
$M_\mathbb{L}$ can be used as a ``Dirac'' operator for the reduced
group C*algebra $C_r^*(G)$. It defines a
Lipschitz seminorm on $C_r^*(G)$, which defines a metric on the
state space of
$C_r^*(G)$. We show that
for any length function satisfying a strong form of polynomial
growth on a discrete group,
the topology from this metric
coincides with the
weak$*$ topology (a key property for the
definition of a ``compact quantum metric
space''). In particular, this holds for all wordlength functions
on finitely generated nilpotentbyfinite groups.
Keywords:group C*algebra, Dirac operator, quantum metric space, discrete nilpotent group, polynomial growth Categories:46L87, 20F65, 22D15, 53C23, 58B34 

4. CMB 2010 (vol 53 pp. 629)
5. CMB 2003 (vol 46 pp. 268)
 Puls, Michael J.

Group Cohomology and $L^p$Cohomology of Finitely Generated Groups
Let $G$ be a finitely generated, infinite group, let $p>1$, and let
$L^p(G)$ denote the Banach space $\{ \sum_{x\in G} a_xx \mid \sum_{x\in
G} a_x ^p < \infty \}$. In this paper we will study the first
cohomology group of $G$ with coefficients in $L^p(G)$, and the first
reduced $L^p$cohomology space of $G$. Most of our results will be for a
class of groups that contains all finitely generated, infinite nilpotent
groups.
Keywords:group cohomology, $L^p$cohomology, central element of infinite order, harmonic function, continuous linear functional Categories:43A15, 20F65, 20F18 
