大多数大型映射类组都不能使用Tits

IF 0.6 3区数学 Q3 MATHEMATICS

Algebraic and Geometric Topology Pub Date : 2020-12-02 DOI:10.2140/agt.2021.21.3675

Daniel Allcock

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引用次数: 2

摘要

设X是一个曲面，可能有边界。假设它有无穷个亏格或无穷多个点，或者一个封闭子集，它是一个从其内部移除了康托集的圆盘。例如，$X$可以是只有有限个边界分量的无限型曲面。我们证明了$X$的映射类组不满足Tits的可选性。也就是说，Map$(X)$包含一个有限生成的子群，该子群实际上是不可解的，并且不包含非abel自由群。

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Most big mapping class groups fail the Tits alternative

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.

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来源期刊

Algebraic and Geometric Topology 数学-数学

CiteScore

1.10

自引率

14.30%

发文量

审稿时长

6-12 weeks

期刊介绍： Algebraic and Geometric Topology is a fully refereed journal covering all of topology, broadly understood.