三维流形群的字问题的几何
Geometry of the word problem for 3-manifold groups
摘要：
我们提供了一个算法来解决的字问题在所有基本群的封闭3-流形，特别是，我们表明，这些群体是autostackable。这提供了一个共同的框架，解决字问题在任何封闭的3-流形组使用有限状态自动机。我们还介绍了一个群的概念，这是autostackable尊重一个子群，并表明，一个基本群的群的顶点群是autostackable尊重任何棱道群是autostackable。一个群，是强陪集自动的autostackable子群，使用前缀闭断面，也被证明是autostackable尊重该子群。安托林和Ciobanu的工作的基础上，我们表明，一个有限生成群，是双曲相对于一个集合的阿贝尔子群也强陪集自动相对于每个子群的集合。最后，我们证明了紧致几何3-流形的基本群，其边界由许多不可压缩的环面组成，是关于任意选择的外围子群的自堆叠的。
英文摘要：
We provide an algorithm to solve the word problem in all fundamental groups of closed 3-manifolds; in particular, we show that these groups are autostackable. This provides a common framework for a solution to the word problem in any closed 3-manifold group using finite state automata. We also introduce the notion of a group which is autostackable respecting a subgroup, and show that a fundamental group of a graph of groups whose vertex groups are autostackable respecting any edge group is autostackable. A group that is strongly coset automatic over an autostackable subgroup, using a prefix-closed transversal, is also shown to be autostackable respecting that subgroup. Building on work by Antolin and Ciobanu, we show that a finitely generated group that is hyperbolic relative to a collection of abelian subgroups is also strongly coset automatic relative to each subgroup in the collection. Finally, we show that fundamental groups of compact geometric 3-manifolds, with boundary consisting of (finitely many) incompressible torus components, are autostackable respecting any choice of peripheral subgroup.
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