无向几何函子
Unoriented geometric functors
摘要：
Farrell和Hsiang注意到，Wall在第9章中定义的几何手术组并不具有Wall所声称的自然性。他们能够通过扩充沃尔的定义来跟踪线丛来解决这个问题。几何墙群的定义涉及同调与当地的系数，这些也缺乏墙的声称自然。人们会希望，涉及非可定向流形的几何边界理论能像局部系数同调理论那样，具有同样的自然性。本文提出了一个设置这种自然完全在当地的系数。将这个理论应用到不可定向的Wall群的例子中，可以恢复Wall最初方法的许多优雅。进而给出了群元共轭诱导映射的几何判定。
英文摘要：
Farrell and Hsiang noticed that the geometric surgery groups defined By Wall, Chapter 9, do not have the naturality Wall claims for them. They were able to fix the problem by augmenting Wall's definitions to keep track of a line bundle. The definition of geometric Wall groups involves homology with local coefficients and these also lack Wall's claimed naturality. One would hope that a geometric bordism theory involving non-orientable manifolds would enjoy the same naturality as that enjoyed by homology with local coefficients. A setting for this naturality entirely in terms of local coefficients is presented in this paper. Applying this theory to the example of non-orientable Wall groups restores much of the elegance of Wall's original approach. Furthermore, a geometric determination of the map induced by conjugation by a group element is given.
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。
