置换模作为CW复形同调的实现
Realization of permutation modules as homology of CW-complexes
- Nankai University（南开大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文研究置换模作为CW复形同调的实现问题，对任意群和特定次数的置换模给出部分解答，并完整解答了Kahn问题。
AI中文摘要：
本文研究了可实现性问题，即要求将作用于分次模的群实现为作用于其同调群的CW复形自同伦等价群。我们在任意群和集中于特定次数的置换模情形下给出了部分回答。作为推论，我们还对任意连通性的CW复形范畴中任意群的Kahn可实现性问题给出了完整回答。
英文摘要：
In this paper, we investigate the realizability problem, which asks whether prescribed group actions on graded modules can be realized by the groups of self-homotopy equivalences of CW-complexes acting on their homology. We provide a partial answer in the case of arbitrary groups and permutation modules concentrated in certain degrees. As a consequence, we realize every group as the group of self-homotopy equivalences of an $R$-local CW-complex with arbitrary prescribed connectivity, where $R$ may be chosen with $ρ(R)$ sufficiently large. In particular, this provides a complete answer to Kahn's realizability problem.
