Sufficient Conditions for Recognizing a 3-manifold Group

Details Sufficient Conditions for Recognizing a 3-manifold Group Sufficient Conditions for Recognizing a 3-manifold Group

2011-08-19

arxiv.org/abs/1108.3881v1

Mathematics

Geometric Topology

28 pages, 18 figures

Scientific paper

In this work we ask when a group is a 3-manifold group, or more speci?cally, when does a group presentation come naturally from a Heegaard diagram for a 3-manifold? We will give some conditions for partial answers to this form of the Isomorphism Problem by addressing how the presentation associated to a diagram for a splitting is related to the fundamental group of a 3-manifold. In the process, we determine an invariant of groups (by way of group presentations) for how far such presentations are from 3-manifolds.

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