A nilmanifold is a quotient of a connected and simply connected nilpotent Lie group G by a uniform lattice N. In this paper, we determine the Reidemeister and Nielsen number of affine n-valued maps on such a nilmanifold. These are maps for which a given lifting to G splits into n affine maps of the Lie group G. To obtain this result we also establish a way of computing the number of generalized twisted conjugacy classes on finitely generated torsion-free nilpotent groups.

中文翻译：

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尼尔森流形上仿射 n 值映射的尼尔森数

尼尔流形是连通和单连通幂零李群G与均匀晶格N的商。在本文中，我们确定了这种尼尔流形上仿射n值映射的 Reidemeister 和 Nielsen 数。这些映射中，给定的G提升会分裂为李群G的n 个仿射映射。为了获得这个结果，我们还建立了一种计算有限生成的无扭转幂零群上广义扭曲共轭类数量的方法。