论文标题
大多数大型映射课程组未能使山雀替代
Most big mapping class groups fail the Tits Alternative
论文作者
论文摘要
令$ x $为一个表面，可能具有边界。假设它具有无限的属或无限的刺穿，或一个闭合子集，该子集是从其内部移除的带有cantor集的磁盘。例如，$ x $可能是无限类型的任何表面，只有有限的边界组件。我们证明，$ x $的映射类组不能满足山雀的替代方案。也就是说，MAP $（x）$包含一个有限生成的子组，该子组几乎无法解决，并且不包含非亚伯自由组。
Let $X$ be a surface, possibly with boundary. Suppose it has infinite genus or infinitely many punctures, or a closed subset which is a disk with a Cantor set removed from its interior. For example, $X$ could be any surface of infinite type with only finitely many boundary components. We prove that the mapping class group of $X$ does not satisfy the Tits Alternative. That is, Map$(X)$ contains a finitely generated subgroup that is not virtually solvable and contains no nonabelian free group.
