Standard Realizations

  • Toshikazu Sunada
Part of the Surveys and Tutorials in the Applied Mathematical Sciences book series (STAMS, volume 6)


We have so far interpreted how elementary algebraic topology can be used for a set-up of topological crystallography. One can say that our discussion is perfect on the basis of pure reflection. Namely, the idea of topological crystals as a product of conceptual thought satisfies enough the people working in pure mathematics. For practical purposes, however, this situation is unsatisfactory because a topological crystal does not inhabit real space, so it is not visible even for the 3D case if we would leave it intact. For this reason, it is a natural desire to find an “actual shape” of a topological crystal.


Riemannian Manifold Homotopy Class Tight Frame Finite Graph Real Crystal 


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© Springer Japan 2013

Authors and Affiliations

  • Toshikazu Sunada
    • 1
  1. 1.School of Science and TechnologyMeiji UniversityKawasaki-shiJapan

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