论文标题
可溶性算术群中的扭曲共轭
Twisted conjugacy in soluble arithmetic groups
论文作者
论文摘要
组自动形态的雷德米斯特数字编码组的扭曲结合类的数量，并可能产生有关与给定对象相关的空间的自图的信息。在这里，我们解决了2000年代中期贡萨尔维斯（Gonçalves）和王（Wong）提出的一个问题：我们构建了一系列无限的紧凑型连接的索尔夫曼福尔德（不是尼尔曼福尔德（Nilmanifolds）），严格增加了尺寸，并且所有其自我态度的等价均已消失了。为此，我们为可溶性线性群体的突出（无限）家族建立了足够的条件，可以拥有所谓的属性$ r_ \ infty $。特别是，由于Dekimpe，Gonçalves，Kochloukova，Nasybullov，Nasybullov，Taback，Tertooy，Tertooy，Van den Bussche和Wong，我们概括或补充了早期结果，表明许多可溶的$ S $ arithmetic群体都有$ r_ \ iffty $，并提出了这个方向的猜测。
Reidemeister numbers of group automorphisms encode the number of twisted conjugacy classes of groups and might yield information about self-maps of spaces related to the given objects. Here we address a question posed by Gonçalves and Wong in the mid 2000s: we construct an infinite series of compact connected solvmanifolds (that are not nilmanifolds) of strictly increasing dimensions and all of whose self-homotopy equivalences have vanishing Nielsen number. To this end, we establish a sufficient condition for a prominent (infinite) family of soluble linear groups to have the so-called property $R_\infty$. In particular, we generalize or complement earlier results due to Dekimpe, Gonçalves, Kochloukova, Nasybullov, Taback, Tertooy, Van den Bussche, and Wong, showing that many soluble $S$-arithmetic groups have $R_\infty$ and suggesting a conjecture in this direction.
