AI 中文总结
该研究给出闭单连通光滑四维流形上二阶非动力学光滑同伦相干作用的首个例子，通过限制离散圆周群在稳定化\(K3\)曲面上的作用获得，还构造相关扩张并展示特殊边界对合，证明了关于整同调球上自由对合光滑扩张的定理。
AI 中文摘要
我们给出了在闭单连通光滑四维流形上二阶非动力学光滑同伦相干作用的首个例子。此作用通过限制离散圆周群在稳定化\(K3\)曲面上的非平凡光滑同伦相干作用得到。我们还构造了紧致光滑\(4\) - 流形上边界对合的相对非动力学光滑同伦相干扩张。此外，展示了一些边界对合，它们在相同稳定化填充上有局部线性拓扑扩张但无光滑扩张。不过，我们证明了一个类似Wall的定理，表明在通过\(S^2\times S^2\)充分多次稳定化后，整同调球不相交并上的每个自由对合可在任何单连通光滑填充上光滑扩张。
英文摘要
We give the first example of a non-kinetic smooth homotopy coherent action of order two on a closed simply connected smooth four-manifold. This action is obtained by restricting a nontrivial smooth homotopy coherent action of the discrete circle group on a stabilized $K3$ surface. We also construct relatively non-kinetic smooth homotopy coherent extensions of boundary involutions over compact smooth $4$-manifolds. In addition, we exhibit boundary involutions that admit locally linear topological extensions but no smooth extensions over the same stabilized fillings. Nevertheless, we prove a Wall-type theorem showing that every free involution on a disjoint union of integral homology spheres extends smoothly over any simply connected smooth filling after sufficiently many stabilizations by $S^2\times S^2$.
Comments39 pages, 2 figures
