论文标题
尼尔森数字上的平均公式
An Averaging Formula for Nielsen numbers on Infra-Solvmanifolds
论文作者
论文摘要
到目前为止，仅针对特殊类别的solvmanifolds，即类型（R）的Infra-Nilmanifolds和Instrra-Nilmanifolds和Instrra-Solvmanifolds，有一个公式可用于计算尼尔森数量的自图数。在本文中，我们提供了一个一般的平均公式，该公式适用于所有可能的Infra-Solvmanifolds上的所有自图，并在Infra-Nilmanifolds或类型（R）的Instra-Nilmanifolds或Instrra-Solvmanifolds的情况下降低到旧配方。此外，当将Infra-Solvmanifold视为多项式歧管时，我们回想起任何映射与多项式图都是同型的，我们显示了如何根据该多项式图的Jacobian翻译我们的公式。
Until now only for special classes of infra-solvmanifolds, namely infra-nilmanifolds and infra-solvmanifolds of type (R), there was a formula available for computing the Nielsen number of a self-map on those manifolds. In this paper, we provide a general averaging formula which works for all self-maps on all possible infra-solvmanifolds and which reduces to the old formulas in the case of infra-nilmanifolds or infra-solvmanifolds of type (R). Moreover, when viewing an infra-solvmanifold as a polynomial manifold, we recall that any map is homotopic to a polynomial map and we show how our formula can be translated in terms of the Jacobian of that polynomial map.
