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Block Matrix Representation of a Graph Manifold Linking Matrix Using Continued Fractions

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DOI: 10.4236/am.2014.513183    3,106 Downloads   3,867 Views   Citations

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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

López, F. , Efremov, V. and Magdaleno, A. (2014) Block Matrix Representation of a Graph Manifold Linking Matrix Using Continued Fractions. Applied Mathematics, 5, 1894-1902. doi: 10.4236/am.2014.513183.

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