论文标题
瑟斯顿地震流的不对称性
The asymmetry of Thurston's earthquake flow
论文作者
论文摘要
我们表明，瑟斯顿的地震流量是强烈不对称的，因为它的归一化器在模量空间上测得测量的层压束的束束的束束束请尽可能小。 (At the level of Teichmüller space, such automorphisms correspond to homeomorphisms that are equivariant with respect to an automorphism of the mapping class group.) It follows that the earthquake flow does not extend to an $\mathrm{SL}(2,\mathbf{R})$-action of orbifold automorphisms and does not admit continuous renormalization自我对称。特别是，它通过Orbifold地图与TeichmüllerOlocycle流程不合子。这与以前的许多结果形成鲜明对比，最值得注意的是Mirzakhani的定理是地震和TeichmüllerOlocycle流是可测量的。
We show that Thurston's earthquake flow is strongly asymmetric in the sense that its normalizer is as small as possible inside the group of orbifold automorphisms of the bundle of measured geodesic laminations over moduli space. (At the level of Teichmüller space, such automorphisms correspond to homeomorphisms that are equivariant with respect to an automorphism of the mapping class group.) It follows that the earthquake flow does not extend to an $\mathrm{SL}(2,\mathbf{R})$-action of orbifold automorphisms and does not admit continuous renormalization self-symmetries. In particular, it is not conjugate to the Teichmüller horocycle flow via an orbifold map. This contrasts with a number of previous results, most notably Mirzakhani's theorem that the earthquake and Teichmüller horocycle flows are measurably conjugate.
