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arXiv · 1210.2101

Recognizing geometric 3-manifold groups using the word problem

Daniel Groves·Jason Fox Manning·Henry Wilton
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Abstract

Adyan and Rabin showed that most properties of groups cannot be algorithmically recognized from a finite presentation alone. We prove that, if one is also given a solution to the word problem, then the class of fundamental groups of closed, geometric 3-manifolds is algorithmically recognizable. In our terminology, the class of geometric 3-manifold groups is `recursive modulo the word problem'.

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Daniel Groves, Jason Fox Manning, Henry Wilton. 2012-10-07. Recognizing geometric 3-manifold groups using the word problem. https://arxiv.org/abs/1210.2101

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