Algorithm for Fast Calculation of Hirzebruch-Jung Continued Fraction Expansions to Coding of Graph Manifolds

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References

[1] Hirzebruh, F. (1971) Differentiable Manifolds and Quadratic Forms. Marcel Dekker, New York.

[2] Popescu-Pampu, P. (2007) The Geometry of Continued Fractions and the Topology of Surface Singularities. Advanced Studies in Pure Mathematics, 46.

[3] Griguolo, L., Seminara, D., Szabo, R.J. and Tanzini, A. (2007) Black Holes, Instanton Counting on Toric Singularities and q-Deformed Two-Dimensional Yang-Mills Theory. Nuclear Physics B, 772, 1-24.

http://dx.doi.org/10.1016/j.nuclphysb.2007.02.030

[4] Saveliev, N. (2002) Fukomoto-Furuta Invariants of Plumbed Homology 3-Spheres. Pacific Journal of Mathematics, 205, 465-490.

http://dx.doi.org/10.2140/pjm.2002.205.465

[5] Becerra, F., Efremov, V. and Hernandez, A. (2014) Block Matrix Representation of a Graph Manifold Linking Matrix Using Continued Fractions. Applied Mathematics, 5, 1894-1902.

http://dx.doi.org/10.4236/am.2014.513183

[6] Neumann, W. (1981) A Calculus for Plumbing Applied to the Topology of Complex Surface Singularities and Degenerating Complex Curves. Transactions of the American Mathematical Society, 268, 299-344.

http://dx.doi.org/10.1090/S0002-9947-1981-0632532-8

[7] Saveliev, N. (2002) Invariants for Homology 3-Spheres. Springer, Berlin.

http://dx.doi.org/10.1007/978-3-662-04705-7

[8] Wen, X.G. and Zee, A. (1992) Classification of Abelian Quantum Hall States and Matrix Formulation of Topological Fluids. Physical Review B, 46, 2290.

http://dx.doi.org/10.1103/PhysRevB.46.2290

[9] Balachandran, A.P., Chandar, L. and Sathiapalan, B. (1995) Chern-Simons Duality and Quantum Hall Effect. Nuclear Physics B, 443, 465-500.

http://dx.doi.org/10.1016/0550-3213(95)00122-9

[10] Fujita, M., Li, W., Ryu, S. and Takayanagi, T. (2009) Fractional Quantum Hall Effect via Holography: Chern-Simons, Edge States, and Hierarchy. Journal of High Energy Physics, 2009, JHEP06.

http://dx.doi.org/10.1088/1126-6708/2009/06/066

[11] Harvey, J.A., Kutasov, D., Martinec, E.J. and Moore, G. (2001) Localized Tachyons and RG Flows.
arXiv: hep-th/0111154v2.

[12] Efremov, V.N., Mitskievich, N.V., Hernandez Magdaleno, A.M. and Serrano Bautista, R. (2005) Topological Gravity on Plumbed V-Cobordism. Classical and Quantum Gravity, 22, 3725.

http://dx.doi.org/10.1088/0264-9381/22/17/022

[13] Efremov, V.N., Hernandez Magdaleno, A.M. and Moreno, C. (2010) Topological Origin of the Coupling Constants Hierarchy in Kaluza-Klein Approach. International Journal of Modern Physics A, 25, 2699.

http://dx.doi.org/10.1142/S0217751X10048482

[14] Efremov, V., Hernandez, A. and Becerra, F. (2014) The Universe as a Set of Topological Fluids with Hierarchy and Fine Tuning of Coupling Constants in Terms of Graph Manifolds. arXiv:1309.0690v2.

[15] Tegmark, M., Aguirre, A., Rees, J. and Wilczek, F. (2006) Dimensionless Constants, Cosmology and Other Dark Matter. Physical Review D, 73, Article ID: 023505.

http://dx.doi.org/10.1103/PhysRevD.73.023505

[16] Bousso, R. (2007) TASI Lectures on the Cosmological Constant. arXiv: hep-th/0708.4231.

[17] Neumann, W. (1997) Commensurability and Virtual Fibration for Graph Manifolds. Topology, 36, 355-378.

http://dx.doi.org/10.1016/0040-9383(96)00014-6

[18] Diamantini, M.C. and Trugenberger, C.A. (2015) Higgsless Superconductivity from Topological Defects in Compact BF Terms. Nuclear Physics B, 891, 401-419.

http://dx.doi.org/10.1016/j.nuclphysb.2014.12.010