Thurston 地震流的非对称性
The asymmetry of Thurston's earthquake flow
AI总结：
本文证明 Thurston 地震流在 orbifold 自同构群中正规化子极小，因而不能扩展为 SL(2,R)-作用，也不具有连续重整化自对称，与 Mirzakhani 的可测共轭结果形成对比。
摘要：
我们证明 Thurston 地震流是强非对称的，其意义在于，在模空间上测地叶状结构丛的 orbifold 自同构群中，它的正规化子尽可能小。（在 Teichmüller 空间层面，这类自同构对应于关于映射类群的一个自同构等变的自同胚。）由此可知，地震流不能扩展为 orbifold 自同构的 $\mathrm{SL}(2,\mathbf{R})$-作用，也不存在连续的重整化自对称。特别地，它不能通过 orbifold 映射共轭于 Teichmüller 环流。这与若干先前结果形成对比，最著名的是 Mirzakhani 的定理：地震流与 Teichmüller 环流是可测共轭的。
英文摘要：
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.
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