Proper actions on $\ell^p$ spaces for relatively hyperbolic groups

一致Lipschitz双曲群在$\ell^p$上的作用

Uniformly Lipschitz Hyperbolic Group Actions on $\ell^p$

本文证明有限生成双曲群在$\ell^p$上存在压缩指数为$1/p$的恰当一致Lipschitz仿射作用，其中$p<Q/(Q-1)$，空间由边界填充上的马尔可夫链构造。

双曲性与有值上同调

Hyperbolicity and bounded-valued cohomology

本文推广 Gersten 的 $\ell^{\infty}$-上同调限制映射满射定理，并据此给出双曲群子群、拟等距区分及上同调计算的应用，同时建立 $FP_2(\mathbb Q)$ 型群等情形的双曲性判据。

椭圆韦伊群的双曲覆盖

The hyperbolic cover of an elliptic Weyl group

本文研究了椭圆韦伊系统双曲覆盖的结构及其与扩展柯西特系统的同构性，并建立了加权射影线的厚子范畴与偏序集之间的双射关系。

Hyperbolic group $C^*$-algebras and free-product $C^*$-algebras as compact quantum metric spaces

Let $\ell$ be a length function on a group G, and let $M_{\ell}$ denote the operator of pointwise multiplication by $\ell$ on $\bell^2(G)$. Following Connes, $M_{\ell}$ can be used as a ``Dirac'' operator for $C_r^*(G)$. It defines a Lipschitz seminorm on $C_r^*(G)$, which defines a metric on the state space of $C_r^*(G)$. We show that if G is a hyperbolic group and if $\ell$ is a word-length function on G, then the topology from this metric coincides with the weak-* topology (our definition of a ``compact quantum metric space''). We show that a convenient framework is that of filtered $C^*$-a…

任意双曲类型的不可定向正则超地图

Non-orientable regular hypermaps of arbitrary hyperbolic type

本文将三角群剩余有限性在可定向曲面上的结论推广至不可定向情形，证明对任意双曲类型均存在无穷多自同构群同构于PSL(2,p)的正则超地图，且此类超地图的承载曲面必为不可定向。

Invariant random subgroups of groups acting on hyperbolic spaces

Suppose that a group $G$ acts non-elementarily on a hyperbolic space $S$ and does not fix any point of $\partial S$. A subgroup $H\le G$ is said to be geometrically dense in $G$ if the limit sets of $H$ and $G$ coincide and $H$ does not fix any point of $\partial S$. We prove that every invariant random subgroup of $G$ is either geometrically dense or contained in the elliptic radical (i.e., the maximal normal elliptic subgroup of $G$). In particular, every ergodic measure preserving action of an acylindrically hyperbolic group on a Borel probability space $(X,μ)$ either has finite stabilizers…

上同调对超几何性的特征化

Cohomological characterisation of hyperbolicity

本文通过上同调理论特征化超几何空间，并推广到相对情形，提出无回路超几何性的上同调特征化方法。

Embeddings of SL(2,Z) into the Cremona group

Geometric and dynamic properties of embeddings of SL(2,Z) into the Cremona group are studied. Infinitely many non-conjugate embeddings which preserve the type (i.e. which send elliptic, parabolic and hyperbolic elements onto elements of the same type) are provided. The existence of infinitely many non-conjugate elliptic, parabolic and hyperbolic embeddings is also shown. In particular, a group G of automorphisms of a smooth surface S obtained by blowing-up 10 points of the complex projective plane is given. The group G is isomorphic to SL(2,Z), preserves an elliptic curve and all its elements …

超几何群上的算子值Haagerup不等式

An Operator-Valued Haagerup Inequality for Hyperbolic Groups

研究超几何群上的算子值Haagerup不等式，改进Buchholz的结果，用单词分解关联的矩阵范数替代原不等式中的ℓ²范数。