尼尔森均衡器理论
Nielsen equalizer theory
摘要：
我们将重合集的Nielsen理论推广到均衡集，即给定的一组（多于2个）映射一致的点。在流形上，这个理论只对不同维数空间之间的映射有意义，我们的结果对从（k-1）n维到n维的紧致流形上的k映射集也成立。我们定义了Nielsen均衡器数，它是当映射被同伦改变时均衡器点的最小数目的下界，并且当域流形不是曲面时实际上等于这个最小数目。作为应用，我们给出了具有正余维的Nielsen符合理论的一些结果.这包括一个完整的计算几何尼尔森数之间的映射环面。
英文摘要：
We extend the Nielsen theory of coincidence sets to equalizer sets, the points where a given set of (more than 2) mappings agree. On manifolds, this theory is interesting only for maps between spaces of different dimension, and our results hold for sets of k maps on compact manifolds from dimension (k-1)n to dimension n. We define the Nielsen equalizer number, which is a lower bound for the minimal number of equalizer points when the maps are changed by homotopies, and is in fact equal to this minimal number when the domain manifold is not a surface. As an application we give some results in Nielsen coincidence theory with positive codimension. This includes a complete computation of the geometric Nielsen number for maps between tori.
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