自由群的几何性和多边形性
Geometricity and Polygonality in Free Groups
摘要：
Gordon和Wilton最近证明了一个自由群F沿着F的一个循环子群C合并的双D包含一个曲面群，如果C的生成元w满足一个称为虚几何性的3-流形理论条件。Wilton和作者定义了W的连续性，它也保证了D中曲面群的存在。本文证明了虚几何性在降阶到有限指数子群F'并在F'上应用自同构时是等价的。从曼宁以前考虑过的一个例子可以看出，相反的情况并不成立。
英文摘要：
Gordon and Wilton recently proved that the double D of a free group F amalgamated along a cyclic subgroup C of F contains a surface group if a generator w of C satisfies a certain 3-manifold theoretic condition, called virtually geometricity. Wilton and the author defined the polygonality of w which also guarantees the existence of a surface group in D. In this paper, virtual geometricity is shown to imply polygonality up to descending to a finite-index subgroup F' and applying an automorphism on F'. That the converse does not hold will follow from an example formerly considered by Manning.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
