几何非柔性性与纤维化于圆周的三维流形
几何拓扑
2014-12-17 v2 微分几何
摘要
我们证明了双曲三维流形是几何非柔性的：一个Kleinian群的单位拟共形形变可以延拓为一个等变双Lipschitz微分同胚，该微分同胚在商空间之间的逐点双Lipschitz常数，对于厚部中的点，随着距凸核边界的距离呈指数衰减。薄部中点的估计由短曲线上复长度的类似估计控制。我们利用这种非柔性性，给出了闭曲面拟Fuchsian空间上伪Anosov双迭代收敛性的新证明，以及由此得到的具有伪Anosov单值性的闭纤维化于圆周的三维流形的双曲化定理。
引用
@article{arxiv.0901.3870,
title = {Geometric inflexibility and 3-manifolds that fiber over the circle},
author = {Jeffrey Brock and Kenneth Bromberg},
journal= {arXiv preprint arXiv:0901.3870},
year = {2014}
}
备注
52 pages. Final version. Appeared in Journal of Topology. Material in original version on inflexibility of hyperbolic cone-manifolds has been rewritten into a new paper with identifier arXiv:1412.4635