TITLE:
Block Matrix Representation of a Graph Manifold Linking Matrix Using Continued Fractions
AUTHORS:
Fernando I. Becerra López, Vladimir N. Efremov, Alfonso M. Hernandez Magdaleno
KEYWORDS:
Graph Manifolds, Continued Fractions, Laplacian Matrices, Kaluza-Klein
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.13,
July
8,
2014
ABSTRACT: We consider the block matrices and 3-dimensional graph manifolds
associated with a special type of tree graphs. We demonstrate that the linking
matrices of these graph manifolds coincide with the reduced matrices obtained
from the Laplacian block matrices by means of Gauss partial diagonalization
procedure described explicitly by W. Neumann. The linking matrix is an
important topological invariant of a graph manifold which is possible to
interpret as a matrix of coupling constants of gauge interaction in
Kaluza-Klein approach, where 3-dimensional graph manifold plays the role of
internal space in topological 7-dimensional BF theory. The Gauss-Neumann method
gives us a simple algorithm to calculate the linking matrices of graph
manifolds and thus the coupling constants matrices.