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Geometry of the word problem for 3-manifold groups. (arXiv:1609.06253v2 [math.GR] UPDATED)
来源于:arXiv
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 consistin 查看全文>>