论文标题
模棱两可的粗（共同）同源理论
Equivariant Coarse (Co-)Homology Theories
论文作者
论文摘要
我们提出了一个艾伦贝格·斯蒂恩（Eilenberg-Steenrod）样的公理框架，用于模棱两可的粗糙同源性和同源理论。我们还讨论了从拓扑理论和相关的侵犯图的一般结构。本文的很大一部分致力于展示一些公认的粗糙（共同）同源性理论，这些理论的模棱两可的版本已经知道，要么将在本文中引入，因此适合此设置。此外，给出了一个更新的，更灵活的粗糙同型概念，它更多地是拓扑同位素的精神。在这些新的同义下，有些但不是全部，粗略的（共同）同源性理论甚至是不变的。他们还使我们提出了一个有意义的概念，即在粗空间上局部紧凑的群体的拓扑作用。
We present an Eilenberg-Steenrod-like axiomatic framework for equivariant coarse homology and cohomology theories. We also discuss a general construction of such coarse theories from topological ones and the associated transgression maps. A large part of this paper is devoted to showing how some well-established coarse (co-)homology theories, whose equivariant versions are either already known or will be introduced in this paper, fit into this setup. Furthermore, a new and more flexible notion of coarse homotopy is given which is more in the spirit of topological homotopies. Some, but not all, coarse (co-)homology theories are even invariant under these new homotopies. They also led us to a meaningful concept of topological actions of locally compact groups on coarse spaces.
