1. CMB 2010 (vol 53 pp. 706)
|Non-Right-Orderable 3-Manifold Groups|
We exhibit infinitely many hyperbolic $3$-manifold groups that are not right-orderable.
Categories:20F60, 57M05, 57M50
2. CMB 2006 (vol 49 pp. 36)
|Holomorphic Frames for Weakly Converging Holomorphic Vector Bundles |
Using a modification of Webster's proof of the Newlander--Nirenberg theorem, it is shown that, for a weakly convergent sequence of integrable unitary connections on a complex vector bundle over a complex manifold, there is a subsequence of local holomorphic frames that converges strongly in an appropriate Holder class.
Categories:57M50, 58E20, 53C24
3. CMB 2004 (vol 47 pp. 332)
|Recurrent Geodesics in Flat Lorentz $3$-Manifolds |
Let $M$ be a complete flat Lorentz $3$-manifold $M$ with purely hyperbolic holonomy $\Gamma$. Recurrent geodesic rays are completely classified when $\Gamma$ is cyclic. This implies that for any pair of periodic geodesics $\gamma_1$, $\gamma_2$, a unique geodesic forward spirals towards $\gamma_1$ and backward spirals towards $\gamma_2$.
Keywords:geometric structures on low-dimensional manifolds, notions of recurrence
4. CMB 2003 (vol 46 pp. 265)
|Reducing Spheres and Klein Bottles after Dehn Fillings |
Let $M$ be a compact, connected, orientable, irreducible 3-manifold with a torus boundary. It is known that if two Dehn fillings on $M$ along the boundary produce a reducible manifold and a manifold containing a Klein bottle, then the distance between the filling slopes is at most three. This paper gives a remarkably short proof of this result.
Keywords:Dehn filling, reducible, Klein bottle
5. CMB 1997 (vol 40 pp. 204)
|The $\eta$-invariants of cusped hyperbolic $3$-manifolds |
In this paper, we define the $\eta$-invariant for a cusped hyperbolic $3$-manifold and discuss some of its applications. Such an invariant detects the chirality of a hyperbolic knot or link and can be used to distinguish many links with homeomorphic complements.
Categories:57M50, 53C30, 58G25