2011/08/19 by Karoline P. Null, Null, Karoline P.
Mathematics · #20B10 #20B40 #22F30 #22F50 #57M05 #57M27 #57N65 #68W99 #FOS: Mathematics #General Topology (math.GN) #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.1108.3881
openalex publication_date 2011/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work we ask when a group is a 3-manifold group, or more specifically, 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.