Expand all Collapse all | Results 1 - 9 of 9 |
1. CMB Online first
Left-orderable 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 two-bridge knot corresponding to the rational number $3/7$, has left-orderable
fundamental group if the slope $r$ satisfies $0\le r \le 4$.
Keywords:left-ordering, Dehn surgery Categories:57M25, 06F15 |
2. CMB Online first
Left-orderable 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 two-bridge knot corresponding to the rational number $3/7$, has left-orderable
fundamental group if the slope $r$ satisfies $0\le r \le 4$.
Keywords:left-ordering, Dehn surgery Categories:57M25, 06F15 |
3. CMB 2013 (vol 57 pp. 310)
Left-orderable 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 two-bridge knot corresponding to the rational number $3/7$, has left-orderable
fundamental group if the slope $r$ satisfies $0\le r \le 4$.
Keywords:left-ordering, Dehn surgery Categories:57M25, 06F15 |
4. CMB 2012 (vol 56 pp. 850)
Left-orderability and Exceptional Dehn Surgery on Twist Knots We show that any exceptional non-trivial Dehn surgery on a twist knot, except the trefoil,
yields a $3$-manifold whose fundamental group is left-orderable.
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:left-ordering, twist knot, Dehn surgery Categories:57M25, 06F15 |
5. CMB 2011 (vol 54 pp. 283)
Surgery on $\widetilde{\mathbb{SL}} \times \mathbb{E}^n$-Manifolds We show that closed $\widetilde{\mathbb{SL}} \times \mathbb{E}^n$-manifolds
are topologically rigid if $n\geq 2$, and are rigid up to
$s$-cobordism, if $n=1$.
Keywords:topological rigidity, geometric structure, surgery groups Categories:57R67, 57N16 |
6. CMB 2010 (vol 54 pp. 556)
Cyclic Surgery Between Toroidal Surgeries
We show that there is an infinite family of hyperbolic knots such that
each knot admits a cyclic surgery $m$ whose adjacent surgeries $m-1$
and $m+1$ are toroidal. This gives an affirmative answer to a
question asked by Boyer and Zhang.
Keywords:cyclic surgery, toroidal surgery Category:57M25 |
7. CMB 2008 (vol 51 pp. 508)
A Result in Surgery Theory We study the topological $4$-dimensional surgery problem
for a closed connected orientable
topological $4$-manifold $X$ with vanishing
second homotopy and $\pi_1(X)\cong A * F(r)$, where $A$ has
one end and $F(r)$ is the free group of rank $r\ge 1$.
Our result is related to a theorem of Krushkal and Lee, and
depends on the validity of the Novikov conjecture for
such fundamental groups.
Keywords:four-manifolds, homotopy type, obstruction theory, homology with local coefficients, surgery, normal invariant, assembly map Categories:57N65, 57R67, 57Q10 |
8. CMB 2006 (vol 49 pp. 624)
On Non-Integral Dehn Surgeries Creating Non-Orientable Surfaces For a non-trivial knot in the $3$-sphere,
only integral Dehn surgery can create a closed $3$-manifold containing a projective plane.
If we restrict ourselves to hyperbolic knots, the corresponding claim for a Klein bottle is still true.
In contrast to these, we show that non-integral surgery on a hyperbolic knot
can create a closed non-orientable surface of any genus greater than two.
Keywords:knot, Dehn surgery, non-orientable surface Category:57M25 |
9. CMB 2003 (vol 46 pp. 356)
Branched Covers of Tangles in Three-balls We give an algorithm for a surgery description of a $p$-fold cyclic branched
cover of $B^3$ branched along a tangle. We generalize constructions of
Montesinos and Akbulut-Kirby.
Keywords:tangle, branched cover, surgery, Heegaard decomposition Categories:57M25, 57M12 |