Abstract: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. As a key tool we construct a hyperbolic graph on which these groups act, which is the analog of the curve graph for the mapping class group.

---

中文翻译：

---

表面微分同胚群上的拟态射

摘要：我们证明了一个正属封闭定向面的微分同胚群的恒等分允许许多无界拟态射。作为推论，我们还推导出该群不是一致完美的，其分裂范数是无界的，回答了 Burago-Ivanov-Polterovich 的问题。作为一个关键工具，我们构建了一个这些组作用于其上的双曲线图，它是映射类组的曲线图的类比。

---