1. CMB 2017 (vol 60 pp. 830)
 Motegi, Kimihiko; Teragaito, Masakazu

Generalized Torsion Elements and Biorderability of 3manifold Groups
It is known that a biorderable group has no generalized torsion
element,
but the converse does not hold in general.
We conjecture that the converse holds for the fundamental groups
of $3$manifolds,
and verify the conjecture for nonhyperbolic, geometric $3$manifolds.
We also confirm the conjecture for some infinite families of
closed hyperbolic $3$manifolds.
In the course of the proof,
we prove that each standard generator of the Fibonacci group
$F(2, m)$ ($m \gt 2$) is a generalized torsion element.
Keywords:generalized torsion element, biordering, 3manifold group Categories:57M25, 57M05, 06F15, 20F05 

2. CMB 2016 (vol 59 pp. 472)
 Clay, Adam; Desmarais, Colin; Naylor, Patrick

Testing Biorderability of Knot Groups
We investigate the biorderability of twobridge knot groups
and the groups of knots with 12 or fewer crossings by applying
recent theorems of Chiswell, Glass and Wilson.
Amongst all knots with 12 or fewer crossings (of which there
are 2977), previous theorems were only able to determine biorderability
of 499 of the corresponding knot groups. With our methods we
are able to deal with 191 more.
Keywords:knots, fundamental groups, orderable groups Categories:57M25, 57M27, 06F15 

3. CMB Online first


Leftorderable fundamental group and Dehn surgery on the knot $5_2$
We show that the resulting manifold by $r$surgery on the knot $5_2$, which is
the twobridge knot corresponding to the rational number $3/7$, has leftorderable
fundamental group if the slope $r$ satisfies $0\le r \le 4$.
Keywords:leftordering, Dehn surgery Categories:57M25, 06F15 

4. CMB Online first


Leftorderable fundamental group and Dehn surgery on the knot $5_2$
We show that the resulting manifold by $r$surgery on the knot $5_2$, which is
the twobridge knot corresponding to the rational number $3/7$, has leftorderable
fundamental group if the slope $r$ satisfies $0\le r \le 4$.
Keywords:leftordering, Dehn surgery Categories:57M25, 06F15 

5. CMB 2013 (vol 57 pp. 310)
6. CMB 2012 (vol 56 pp. 850)
 Teragaito, Masakazu

Leftorderability and Exceptional Dehn Surgery on Twist Knots
We show that any exceptional nontrivial Dehn surgery on a twist knot, except the trefoil,
yields a $3$manifold whose fundamental group is leftorderable.
This is a generalization of a result of Clay, Lidman and Watson, and
also gives a new supporting evidence for a conjecture of Boyer, Gordon and Watson.
Keywords:leftordering, twist knot, Dehn surgery Categories:57M25, 06F15 
