Topological constructions in the o-graph calculus

Abstract

BENEDETTI and PETRONIO developed in [1] a so called o-Graph Calculus, where a compact oriented 3-manifold with nonempty boundary could be described by a quadrivalent graph together with some extra structure. In this paper, we will show how topological constructions such as puncturing, connected sums, attaching handles, closing boundary components and product and mapping tori constructions can be translated into the o-graph calculus.