Event Type:

Geometry-Topology Seminar

Date/Time:

Monday, February 20, 2017 - 12:00 to 12:45

Location:

BEXL 207

Institution:

Graduate Student

Abstract:

In a previous seminar, George Yancey introduced several equivalent descriptions of three dimensional lens spaces. One of these descriptions was an example of a Heegaard diagram, which is a general way of constructing 3-manifolds. In this talk, we begin with a family of group presentations and an essential spherical map into their model, and show how to construct a Heegaard diagram from this data. The model for the group presentation is the spine of the corresponding 3-manifold, and the group structure determines the geometry of the manifold. Moreover, the resulting manifolds have a cyclic symmetry, and we find they are n-fold cyclic coverings of certain lens spaces. These examples include and extend earlier results of Cavicchioli, Repovs, and Spaggiari from 2003.