1. CJM 2016 (vol 68 pp. 655)
 Klartag, Bo'az; Kozma, Gady; Ralli, Peter; Tetali, Prasad

Discrete Curvature and Abelian Groups
We study a natural discrete Bochnertype inequality on graphs,
and explore its merit as a notion of ``curvature'' in discrete
spaces.
An appealing feature of this discrete version of the socalled
$\Gamma_2$calculus (of BakryÃmery) seems to be that it is
fairly
straightforward to compute this notion of curvature parameter
for
several specific graphs of interest  particularly, abelian
groups, slices of the hypercube, and the symmetric group under
various sets of generators.
We further develop this notion by deriving Busertype inequalities
(Ã la Ledoux), relating functional and isoperimetric constants
associated with a graph.
Our derivations provide a tight bound on the Cheeger constant
(i.e., the edgeisoperimetric constant) in terms of
the spectral gap, for graphs with nonnegative curvature, particularly,
the class of abelian Cayley graphs  a result of independent
interest.
Keywords:Ricci curvature, graph theory, abelian groups Categories:53C21, 57M15 

2. CJM 2013 (vol 66 pp. 141)
 CaillatGibert, Shanti; Matignon, Daniel

Existence of Taut Foliations on Seifert Fibered Homology $3$spheres
This paper concerns the problem of existence of taut foliations among $3$manifolds.
Since the contribution of David Gabai,
we know that closed $3$manifolds with nontrivial second homology group
admit a taut foliation.
The essential part of this paper focuses on Seifert fibered homology $3$spheres.
The result is quite different if they are integral or rational but nonintegral homology $3$spheres.
Concerning integral homology $3$spheres, we can see that all but the $3$sphere and the PoincarÃ© $3$sphere admit a taut foliation.
Concerning nonintegral homology $3$spheres,
we prove there are infinitely many which admit a taut foliation, and infinitely many without taut foliation.
Moreover, we show that the geometries do not determine the existence of taut foliations
on nonintegral Seifert fibered homology $3$spheres.
Keywords:homology 3spheres, taut foliation, Seifertfibered 3manifolds Categories:57M25, 57M50, 57N10, 57M15 

3. CJM 2011 (vol 64 pp. 102)
 Ishii, Atsushi; Iwakiri, Masahide

Quandle Cocycle Invariants for Spatial Graphs and Knotted Handlebodies
We introduce a flow of a spatial graph and see how invariants for
spatial graphs and handlebodylinks are derived from those for flowed
spatial graphs.
We define a new quandle (co)homology by introducing a subcomplex of the
rack chain complex.
Then we define quandle colorings and quandle cocycle invariants for
spatial graphs and handlebodylinks.
Keywords:quandle cocycle invariant, knotted handlebody, spatial graph Categories:57M27, 57M15, 57M25 

4. CJM 2004 (vol 56 pp. 1022)
 Matignon, D.; Sayari, N.

NonOrientable Surfaces and Dehn Surgeries
Let $K$ be a knot in $S^3$. This paper is devoted to Dehn surgeries which create
$3$manifolds containing a closed nonorientable surface $\ch S$. We look at the
slope ${p}/{q}$ of the surgery, the Euler characteristic $\chi(\ch S)$ of the
surface and the intersection number $s$ between $\ch S$ and the core of the Dehn
surgery. We prove that if $\chi(\hat S) \geq 15  3q$, then $s=1$. Furthermore,
if $s=1$ then $q\leq 43\chi(\ch S)$ or $K$ is cabled and $q\leq 85\chi(\ch S)$.
As consequence, if $K$ is hyperbolic and $\chi(\ch S)=1$, then $q\leq 7$.
Keywords:Nonorientable surface, Dehn surgery, Intersection graphs Categories:57M25, 57N10, 57M15 

5. CJM 1999 (vol 51 pp. 1035)
 Litherland, R. A.

The Homology of Abelian Covers of Knotted Graphs
Let $\tilde M$ be a regular branched cover of a homology 3sphere
$M$ with deck group $G\cong \zt^d$ and branch set a trivalent graph
$\Gamma$; such a cover is determined by a coloring of the edges of
$\Gamma$ with elements of $G$. For each index2 subgroup $H$ of
$G$, $M_H = \tilde M/H$ is a double branched cover of $M$. Sakuma
has proved that $H_1(\tilde M)$ is isomorphic, modulo 2torsion, to
$\bigoplus_H H_1(M_H)$, and has shown that $H_1(\tilde M)$ is
determined up to isomorphism by $\bigoplus_H H_1(M_H)$ in certain
cases; specifically, when $d=2$ and the coloring is such that the
branch set of each cover $M_H\to M$ is connected, and when $d=3$
and $\Gamma$ is the complete graph $K_4$. We prove this for a
larger class of coverings: when $d=2$, for any coloring of a
connected graph; when $d=3$ or $4$, for an infinite class of
colored graphs; and when $d=5$, for a single coloring of the
Petersen graph.
Categories:57M12, 57M25, 57M15 

6. CJM 1997 (vol 49 pp. 883)