表面微分同胚群上的拟态射

IF 3.5 1区数学 Q1 MATHEMATICS

Journal of the American Mathematical Society Pub Date : 2019-09-12 DOI:10.1090/JAMS/981

Jonathan Bowden, S. Hensel, Richard C. H. Webb

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引用次数: 17

摘要

我们证明了一个正亏格闭定向曲面的微分同胚群的恒等分量允许许多无界拟态射。作为推论，我们还推导出这个群不是一致完美的，它的碎片范数是无界的，回答了Burago Ivanov Polterovich的一个问题。为此，我们从映射类群的理论中引入了曲线图的一个类似物。我们证明了它是双曲的，并且等距的自然群作用满足Bestvina Fujiwara准则。

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Quasi-morphisms on surface diffeomorphism groups

We show that the identity component of the group of diffeomorphisms of a closed oriented surface of positive genus admits many unbounded quasi-morphisms. As a corollary, we also deduce that this group is not uniformly perfect and its fragmentation norm is unbounded, answering a question of Burago-Ivanov-Polterovich. To do this, we introduce an analogue of the curve graph from the theory of mapping class groups. We show that it is hyperbolic and that the natural group action by isometries satisfies the criterion of Bestvina-Fujiwara.

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来源期刊

Journal of the American Mathematical Society 数学-数学

CiteScore

7.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles of the highest quality in all areas of pure and applied mathematics.