同维流形间映射重合指数的公理
Axioms for the coincidence index of maps between manifolds of the same dimension
摘要：
本文从公理化的角度研究了同维两流形之间映射的重合理论。首先，我们看看流形之间的映射的重合，其中一个映射是定向真的，并给出一组公理，以刻画局部指数（这是一个整数值函数）。然后我们考虑两个流形之间任意映射对的重合理论。类似地，我们提供了一组公理的特点，在这种情况下，这是一个功能的地方指数，值在$\Z\oplus \Z_2$。我们还表明，在每一个设置，该组值的索引（无论是$\Z$或$\Z\oplus \Z_2$）是由公理。最后，对于两个流形之间任意映射对的重合理论的一般情况，我们给出了一组公理，它们刻画了依赖于这对函数的阿贝尔群的局部Reidemeister迹。这些结果推广了可定向微分流形重合的已知结果。
英文摘要：
We study the coincidence theory of maps between two manifolds of the same dimension from an axiomatic viewpoint. First we look at coincidences of maps between manifolds where one of the maps is orientation true, and give a set of axioms such that characterizes the local index (which is an integer valued function). Then we consider coincidence theory for arbitrary pairs of maps between two manifolds. Similarly we provide a set of axioms which characterize the local index, which in this case is a function with values in $\Z\oplus \Z_2$. We also show in each setting that the group of values for the index (either $\Z$ or $\Z\oplus \Z_2$) is determined by the axioms. Finally, for the general case of coincidence theory for arbitrary pairs of maps between two manifolds we provide a set of axioms which charaterize the local Reidemeister trace which is an element of an abelian group which depends on the pair of functions. These results extend known results for coincidences between orientable differentiable manifolds.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
