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1. CMB 2011 (vol 54 pp. 283)
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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 |
2. CMB 2004 (vol 47 pp. 332)
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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 Categories:57M50, 37B20 |