1. 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 

2. CJM 2010 (vol 62 pp. 994)
 Breslin, William

Curvature Bounds for Surfaces in Hyperbolic 3Manifolds
A triangulation of a hyperbolic $3$manifold is \emph{Lthick} if each
tetrahedron having all vertices in the thick part of $M$ is
$L$bilipschitz diffeomorphic to the standard Euclidean tetrahedron.
We show that there exists a fixed constant $L$ such that every
complete hyperbolic $3$manifold has an $L$thick geodesic
triangulation. We use this to prove the existence of universal bounds on
the principal curvatures of $\pi_1$injective surfaces and strongly
irreducible Heegaard surfaces in hyperbolic $3$manifolds.
Category:57M50 

3. CJM 2008 (vol 60 pp. 164)
 Lee, Sangyop; Teragaito, Masakazu

Boundary Structure of Hyperbolic $3$Manifolds Admitting Annular and Toroidal Fillings at Large Distance
For a hyperbolic $3$manifold $M$ with a torus boundary component,
all but finitely many Dehn fillings yield hyperbolic $3$manifolds.
In this paper, we will focus on the situation where
$M$ has two exceptional Dehn fillings: an annular filling and a toroidal filling.
For such a situation, Gordon gave an upper bound of $5$ for the distance between such slopes.
Furthermore, the distance $4$ is realized only by two specific manifolds, and $5$
is realized by a single manifold.
These manifolds all have a union of two tori as their boundaries.
Also, there is a manifold with three tori as its boundary which realizes the distance $3$.
We show that if the distance is $3$ then the boundary of the manifold consists of at most three tori.
Keywords:Dehn filling, annular filling, toroidal filling, knot Categories:57M50, 57N10 

4. CJM 2007 (vol 59 pp. 418)
 Stoimenow, A.

On Cabled Knots and Vassiliev Invariants (Not) Contained in Knot Polynomials
It is known that the BrandtLickorishMillettHo polynomial $Q$
contains Casson's knot invariant. Whether there are (essentially)
other Vassiliev knot invariants obtainable from $Q$ is an open
problem. We show that this is not so up to degree $9$. We also
give the (apparently) first examples of knots not distinguished
by 2cable HOMFLY polynomials which are not mutants. Our calculations
provide evidence of a negative answer to the question whether Vassiliev
knot invariants of degree $d \le 10$ are determined by the HOMFLY and
Kauffman polynomials and their 2cables, and for the existence of
algebras of such Vassiliev invariants not isomorphic to the algebras
of their weight systems.
Categories:57M25, 57M27, 20F36, 57M50 

5. CJM 2006 (vol 58 pp. 673)
 Bart, Anneke; Scannell, Kevin P.

The Generalized Cuspidal Cohomology Problem
Let $\Gamma \subset \SO(3,1)$ be a lattice.
The well known \emph{bending deformations}, introduced by
\linebreak Thurston
and Apanasov, can be used
to construct nontrivial curves of representations of $\Gamma$
into $\SO(4,1)$ when $\Gamma \backslash \hype{3}$ contains
an embedded totally geodesic surface. A tangent vector to such a
curve is given by a nonzero group cohomology class
in $\H^1(\Gamma, \mink{4})$. Our main result generalizes this
construction of cohomology to the context of ``branched''
totally geodesic surfaces.
We also consider a natural generalization of the famous
cuspidal cohomology problem for the Bianchi groups
(to coefficients in nontrivial representations), and
perform calculations in a finite range.
These calculations lead directly to an interesting example of a
link complement in $S^3$
which is not infinitesimally rigid in $\SO(4,1)$.
The first order deformations of this link complement are supported
on a piecewise totally geodesic $2$complex.
Categories:57M50, 22E40 
