秩一作用的轨道等价的显式构造
Explicit construction of orbit equivalence for rank-one actions
AI总结：
针对离散可数无限群G的两个秩一保测G作用，从切割与堆叠参数出发构造Borel轨道等价，还证明了其在连续(C,F)作用下的拓扑对应，属于动力系统领域的轨道等价研究。
AI中文摘要：
设G为离散可数无限群。给定两个秩一保测G作用，其不变测度均有限或均无限，我们从它们的切割与堆叠参数出发，在不变共零子集上给出Borel轨道等价的直接显式构造。我们还在附加相容性假设下，证明了该结论的拓扑对应，即G在非紧局部紧Cantor空间上的连续(C,F)作用的情形。
英文摘要：
Let $G$ be a discrete countable infinite group. Given two rank-one measure-preserving $G$-actions whose invariant measures are either both finite or both infinite, we give a direct explicit construction, from their cutting-and-stacking parameters, of a Borel orbit equivalence on invariant conull subsets. We also prove a topological counterpart of this assertion, under additional compatibility assumptions, for continuous $(C,F)$-actions of $G$ on non-compact locally compact Cantor spaces.
