Titlebook: Topological Crystallography; With a View Towards Toshikazu Sunada Book 2013 Springer Japan 2013 Covering map.Discrete Abel--Jacobi map.Hom

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Introduction, of the nineteenth century, which, needless to say, has been playing a significant role in the classification of crystals in view of the symmetry. Graph theory is another powerful area for the obvious reason that it is used to study the microscopic structure of a crystal (and any molecule) as a 3D (

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Quotient Objects this concept is the periodic nature of crystal structures with respect to parallel translations; that is, a quotient graph in crystallography is nothing but the quotient graph of a 3D network by the translational action of a lattice group; see the next chapter for details.

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Generalities on Graphsapter, the notion of graphs was implicitly used by Leonhard Euler (1707–1783). Practically, we represent a graph by a diagram in a plane or space consisting of points (vertices) and lines (edges). Lines are allowed to intersect each other. In some applications, say communication networks and electri

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Homology Groups of Graphs(or volume) of two figures, they made up an algebraic system with addition and subtraction performed among a class of figures, e.g., polygons or polyhedra. Figure 4.1 illustrates a way to prove using geometric algebra that the area of a triangle is equal to one-half of the area of a rectangle with t

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Explicit Construction remains to be done is to establish its explicit construction fitting in with the enumeration of topological crystals. The idea is quite simple. We make up a candidate for the building block . by the method suggested in Notes (III) in .. To this end, we shall equip the vector space . of 1-chains wit

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