Daniel Kasprowski
We prove that for every finitely generated subgroup of a virtually connected Lie group which admits a finite dimensional model for the classifying space for proper actions the assembly map in algebraic K-theory is split injective. We also prove a similar statement for algebraic L-theory, which in particular implies the integral Novikov conjecture for such groups.
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On the classifying space of the family of virtually cyclic subgroups
研究了离散群的虚循环子群族的分类空间的最小维数。我们给一个完整的答案，例如，如果该集团几乎是多Z，字双曲或可数本地几乎循环。我们给出的例子群的差异的最小尺寸的分类空间的虚拟循环和有限的子群是-1，0和1，并显示在许多情况下，没有其他的值可以出现。
We give a bound for the geometric dimension for the family of virtually cyclic groups in mapping class groups of a compact surface with punctures, possibly with nonempty boundary and negative Euler characteristic.
On the classifying space for the family of virtually cyclic subgroups for elementary amenable groups
我们表明，基本的顺从的群体，这有一个界的顺序，其有限子群，承认有限维模型的分类空间与虚拟循环各向同性。
We give a bound for the virtually cyclic dimension of groups with a normal subgroup of finite index which satisfies that every infinite virtually-cyclic subgroup is contained in a unique maximal such subgroup. As an application we provide a bound for the virtually-cyclic dimension for the braid group of a closed surface with genus greater than 2 and for right-angled Artin groups.
We prove that, for $n\geq 3$, the minimal dimension of a model of the classifying space of the full braid group $B_n$, and of the pure braid group $P_n$, with respect to the family of virtually cyclic groups is $n$.
Geometric dimension of groups for the family of virtually cyclic subgroups
通过研究虚循环群的稳定子，证明了每个有限Hirsch长度h和基数aleph-n的初等顺从群都存在一个有限维分类空间，其虚循环稳定子的维数为n+h+2.我们还提供了一个标准，适合到一个扩张的挠自由商的群体，承认一个有限维分类空间与虚拟循环稳定。最后，我们展示了F型整线性群的例子，其几何尺寸的家庭的虚拟循环子群是有限的，但任意大于几何尺寸的适当行动。这回答了W.卢克
On the classifying space of the family of finite and of virtually cyclic subgroups for CAT(0)-groups
设G是在完备CAT（0）-空间X上适当等距作用的离散群。考虑一个整数d，其中d=1或d大于或等于3，使得X的拓扑维数以d为界。证明了dim（E_fin（G））小于或等于d的真G-作用的分类空间的G-CW-模型E_fin（G）的存在性.在作用也是余紧的条件下，证明了虚循环子群族的分类空间存在G-CW模型E_vcyc（G），使得dim（E_vcyc（G））小于或等于d+1.
Classifying spaces with virtually cyclic stabilizers for linear groups
证明了$\mathrm{GL}(n,\mathbb{R})$的每个离散子群都有一个具有虚循环稳定子的有限维分类空间。将我们的方法应用于$\mathrm{SL}(3,\mathbb{Z})$，得到了一个具有虚循环稳定子的四维分类空间及其群环的代数$K$ -理论的分解.
Classifying spaces for families of virtually abelian subgroups of surface braid groups
本文研究了表面纯辫群虚阿贝尔子群族的分类空间的最小维数，证明其等于群的虚上同调维数加n，并应用于计算可算子群族的分类空间最小维数。
We show that a countable group is locally virtually cyclic if and only if its Bredon cohomological dimension for the family of virtually cyclic subgroups is at most one.
On The Dimension of The Virtually Cyclic Classifying Space of a Crystallographic Group
本文构造了一个n秩结晶群G相对于G的虚循环子群族VC的分类空间BVCG的模型。利用该模型证明了对于维数小于vcd（G）+1的G的虚循环分类空间不存在其它模型，其中vcd（G）表示G的虚上同调维数.此外，我们的建筑尺寸实现了这一限制。
The Virtually Cyclic Classifying Space of the Heisenberg Group
我们感兴趣的虚拟cohomological尺寸（或vcd）的离散组伽玛和最小可能的尺寸的一个模型的分类空间伽玛相对于其家庭的虚拟循环子群之间的关系。本文构造了Heisenberg群的虚循环分类空间的一个模型。这个模型有3维，等于海森堡群的vcd。我们还证明了不存在维数小于小于3的模型。
This thesis concerns the study of the Bredon cohomological and geometric dimensions of a discrete group $G$ with respect to a family $\mathfrak{F}$ of subgroups of $G$. With that purpose, we focus on building finite-dimensional models for $\operatorname{E}_{\mathfrak{F}} \left( G \right)$. The cases of the family $\mathfrak{Fin}$ of finite subgroups of a group and the family $\mathfrak{VC}$ of virtually cyclic subgroups of a group have been widely studied and many tools have been developed to relate the classifying spaces for $\mathfrak{VC}$ with those for $\mathfrak{Fin}$. Given a discrete gr…
Given a group $G$ and a family of subgroups $\mathcal{F}$, we consider its classifying space $E_{\mathcal F}G$ with respect to $\mathcal{F}$. When $\mathcal F = \mathcal{VC}yc$ is the family of virtually cyclic subgroups, Juan-Pineda and Leary conjectured that a group admits a finite model for this classifying space if and only if it is virtually cyclic. By establishing a connection to conjugacy growth we can show that this conjecture holds for linear groups. We investigate a similar question that was asked by Lück--Reich--Rognes--Varisco for the family of cyclic subgroups. Finally, we constru…
We determine the large scale geometry of the minimal displacement set of a hyperbolic isometry of a systolic complex. As a consequence, we describe the centraliser of such an isometry in a systolic group. Using these results, we construct a low-dimensional classifying space for the family of virtually cyclic subgroups of a group acting properly on a systolic complex. Its dimension coincides with the topological dimension of the complex if the latter is at least four. We show that graphical small cancellation complexes are classifying spaces for proper actions and that the groups acting on them…
We prove the A-theoretic Farrell-Jones Conjecture for virtually solvable groups. As a corollary, we obtain that the conjecture holds for S-arithmetic groups and lattices in almost connected Lie groups.
Given a discrete group $G$, for any integer $r\geqslant0$ we consider the family of all virtually abelian subgroups of $G$ of rank at most $r$. We give an upper bound for the Bredon cohomological dimension of $G$ for this family for a certain class of groups acting on $\mathrm{CAT}(0)$ spaces. This covers the case of Coxeter groups, Right-angled Artin groups, fundamental groups of special cube complexes and graph products of finite groups. Our construction partially answers a question of J.-F. Lafont.
Bredon cohomological dimensions for groups acting on CAT(0)-spaces
设G是拓扑维数有界的可分完备CAT（0）-空间上具有离散轨道的等距作用群。在一定条件下，给出了有限子群族和虚循环子群族G的Bredon上同调维数的上界.作为应用，我们证明了亏格g大于1的任意闭连通可定向曲面的映射类群允许一个具有虚循环稳定子的（9 g-8）维分类空间.此外，我们的结果适用于基本群的图形的群体和群体的欧几里德建筑物。特别地，我们证明了所有正特征的非线性生成的线性群对于真作用有一个有限维的分类空间，对于虚循环子群族有一个有限维的分类空间.我们还表明，每个广义Baumslag-Solitar群有一个3维模型的分类空间与虚拟循环稳定。
Centralisers and the virtually cyclic dimension of $\mathrm{Out}(F_N)$
本文证明了 $\mathrm{Out}(F_N)$ 的有限指标同余子群 $\mathrm{IA}_N(3)$ 的虚循环维数为 $2N-2$，从而推导出 $\mathrm{Out}(F_N)$ 的虚循环维数有限，并证明了 Lück 性质 (C) 及中心化子等相关结论。
Virtually cyclic dimension for 3-manifold groups
该研究针对连通闭可定向3-流形的基本群，明确计算其虚拟循环几何维数，工具涵盖流形分解、推出构造及Bredon上同调计算，解决了3-流形群相关维数的计算问题。
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