Geometry and Topology

Graphic presentations on the lens spaces minimal $DS$-diagrams

M. A. Ovchinnikov

Chelyabinsk State University

Abstract: $DS$-diagram is a three-valent graph on a two-sphere with an identification which glues vertices in fours, edges in threes, faces in twos. Any compact closed 3-manifold can be constructed from the 3-ball by factorizing its boundary according to an appropriate $DS$-diagram. The $DS$-diagrams of lens spaces with minimal number of faces among all known $DS$-diagrams of these manifolds are considered in the work. A few methods of constructing these diagrams as plane graphs with straight edges are described. Advantages of each method are discussed.