1. CMB 2010 (vol 53 pp. 706)
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