AI 中文总结
本文证明了有界几何真度量空间的有限乘积满足粗Novikov猜想，通过构造粗真代数和多阶段Roe代数及指标映射，建立了连接迭代相对指标理论与全局猜想的约化定理。
AI 中文摘要
本文证明了有界几何真度量空间的有限乘积满足粗Novikov猜想，其中每个因子允许纤维粗嵌入到可能不同的目标空间。关键要素是构造适用于乘积空间的合适的粗真代数。我们的另一个主要工具是相对高阶指标理论的迭代方法。通过构造相应的多阶段Roe代数和指标映射，我们建立了一个约化定理，将这些迭代相对陈述与全局粗Novikov猜想联系起来。
英文摘要
In this paper, we prove that the coarse Novikov conjecture holds for finite products of bounded-geometry proper metric spaces whose factors admit fibred coarse embeddings into possibly different target spaces. A key ingredient is the construction of suitable coarsely proper algebras adapted to product spaces. Our other main tool is an iterated approach to relative higher index theory. By constructing the corresponding multi-stage Roe algebras and index maps, we establish a reduction theorem that bridges these iterated relative statements with the global coarse Novikov conjecture.
Comments29pages
