Classification of the Gluing Matrices on the Loop Molecules of the Points of Center-Center Type

Abstract

The Fomenko–Zieschang theory of topological invariants says that the mark r is zero for the points of center-center type. The mark ε is known to be dependent on the orientation of the Q3 manifold, the orientation of the critical circumferences of the Liouville system’s additional integral F, and the orientation of the molecule’s ribs. This article investigates the method of the explicit setting of the basis cycles’ orientation and suggests a way of finding the gluing matrices on the loop molecules of the points of center-center type depending on the allocation of the arcs of the bifurcation diagram.