Japanese Journal of Mathematics

, Volume 7, Issue 1, pp 1–39 | Cite as

Lecture on topological crystallography

Original Articles


This is an expository article on modern crystallography based on discrete geometric analysis, a hybrid field of several traditional disciplines: graph theory, geometry, theory of discrete groups, and probability, which has been developed in the last decade. The mathematical part relying on algebraic topology is fairly elementary, but may be still worthwhile for crystallographers who want to learn how well-established mathematics is effectively used in the practical science. A brief history of crystallography is also explained.

Keywords and phrases

topological crystal canonical placement discrete geometric analysis discrete Abel–Jacobi map 

Mathematics Subject Classification (2010)

05-01 (primary) 05C63 31C20 39A12 74E15 (secondary) 


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Copyright information

© The Mathematical Society of Japan and Springer Japan 2012

Authors and Affiliations

  1. 1.Meiji Institute for Advanced Study of Mathematical SciencesMeiji UniversityKawasakiJapan
  2. 2.WPI Advanced Institute for Material ResearchTohoku UniversitySendaiJapan

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