Dehn扭转类中的有界垂直偏差与无理圆周因子

中文摘要 AI 辅助

我们证明，任何与具有无理有界垂直偏差的Dehn扭转映射同伦的二维环面上的同胚映射都承认一个无理圆周因子。这建立了一个此前由Kocsard研究的刚性性质，他在额外的小游荡域假设下证明了这一蕴含关系。我们证明该假设可以完全去掉：Dehn扭转固有的宏观剪切自然消除了在恒等映射同伦类中无法移除的一般环状障碍。

英文摘要

We prove that a homeomorphism of the two-torus in a Dehn twist homotopy class is a topological extension of an irrational circle rotation if and only if its vertical rotation set reduces to a single irrational number and the homeomorphism exhibits uniformly bounded rotational deviations in the vertical direction. This result has been previously obtained by the second author under an additional hypothesis about the geometry of the non-wandering set. We show that this hypothesis can be entirely dropped: the large-scale shear intrinsic to a Dehn twist eliminates the obstructions coming from the wandering set, which cannot be removed in the homotopy class of the identity. Finally, we prove that the factor is unique up to a circle rotation and is locally constant on the wandering set. Consequently, every connected component of the wandering set is contained in a single fiber, is itself a wandering domain and is either inessential or annular.

发表机构

• IMPA（巴西数学研究所）

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