Mathematics

A three-dimensional manifold defined by a 4-colored graph which is two-fold covering the 4-colored octahedron graph

M. A. Ovchinnikov

Chelyabinsk State University, Chelyabinsk, Russia

Abstract: In the theory of three-dimensional manifolds regular graphs of degree 4 with edges colored by 4 colors is a way to represent 3-manifolds. The manifold defined by some certain symmetric 4-colored graph with 12 vertices is recognized in the work. It is shown that the manifold is homeomorphic to the complement space to the link in 3-sphere consisting of the Borromean link and a standard circle which is the 3-order rotation axis of the Borromean link. Some other natural presentations of the manifold are found. It is shown also that the 4-colored graph is the two-fold covering of the 4-colored octahedron graph.

Keywords: low-dimensional topology, 3-dimensional manifolds, links, 4-colored graphs, closed braids, spines.

UDC: 513.83

Received: 14.05.2016
Revised: 20.05.2016

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