论文标题
粗几何形状中的次级杯子和盖产品
Secondary cup and cap products in coarse geometry
论文作者
论文摘要
我们从给定的十字和倾斜产品的粗（共同）同源性理论上构建了次级杯和盖产品。它们是针对粗间隙定义的，相对于弱的广义受控变形缩回。 关于普通的粗糙同谋，我们的二级杯产品与ROE定义的次级产品一致。为了使拓扑粗糙（共同）同源性理论的重新分解，我们的次级杯子和帽产品对应于希格森（Higson）上的主要杯子和帽子产物，通过侵犯图占主导地位。在粗糙的$ \ mathrm {k} $ - 理论和 - 理论的情况下，辅助产品对应于$ \ mathrm {k} $之间的规范主要产品 - 稳定的Higson Corona和ROE代数的理论和组装下的Roe Algebra。
We construct secondary cup and cap products on coarse (co-)homology theories from given cross and slant products. They are defined for coarse spaces relative to weak generalized controlled deformation retracts. On ordinary coarse cohomology, our secondary cup product agrees with a secondary product defined by Roe. For coarsifications of topological coarse (co-)homology theories, our secondary cup and cap products correspond to the primary cup and cap products on Higson dominated coronas via transgression maps. And in the case of coarse $\mathrm{K}$-theory and -homology, the secondary products correspond to canonical primary products between the $\mathrm{K}$-theories of the stable Higson corona and the Roe algebra under assembly and co-assembly.
