Some conditions for recognizing a 3-manifold group

• Other Authors: Hempel, John
• Format: Others
• Language: English
• Published: 2011
• Subjects: Mathematics
• Online Access: http://hdl.handle.net/1911/62076

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, still using diagrams as a tool to answer these questions. In the process, we determine an invariant of groups (by way of group presentations) for how far such presentations are from 3-manifolds.