AI 中文总结
该研究解决高维非球面流形的Nielsen实现问题，聚焦素数阶循环群作用，通过等变庞加莱对偶空间研究与障碍理论，突破此前仅能处理离散不动点集的局限，实现含高维不动点集的拓扑解。
AI 中文摘要
我们在一类新的特殊情形下解决了高维非球面流形的Nielsen实现问题，主要聚焦于素数阶循环群的作用。其创新之处在于，该方法为具有某些高维不动点集的问题提供了拓扑解，而此前这类问题的解仅限于离散不动点集。这一成果得益于近期与Kirstein合作开展的等变庞加莱对偶空间研究，以及Farrell-Lück-Steimle提出的同伦类中近似纤维丛的障碍理论。
英文摘要
We solve the Nielsen realisation problem for high-dimensional aspherical manifolds in a new class of special cases. Mainly, we focus on actions of cyclic groups of prime order. A novelty is that it gives topological solutions to the problem with certain high-dimensional fixed point sets, whereas previous solutions of this type were restricted to discrete fixed point sets. This is enabled by recent joint work with Kirstein on isovariant Poincaré duality spaces, and Farrell-Lück-Steimle's obstruction theory to finding approximate fibrations within a homotopy class.
Comments35 pages, comments welcome
