A Short Lecture on Topological Crystallography and a Discrete Surface Theory
arXiv:2002.09562
Abstract
This is an unrefereed lecture note based on lectures in 'Introductory Workshop on Discrete Differential Geometry' at Korea University on January 21--24, 2019. In this note, we discuss topological crystallography, which is a mathematical theory of crystal structures. The most symmetric structure among all placements of the graph is obtained by a variational principle in topological crystallography. We also discuss a theory of trivalent discrete surfaces in -dimensional Euclidean space, which are mathematical models of crystal/molecular structures.
44 pages, 38 figures, and 1 table. available at http://math.korea.ac.kr/_res/math/etc/AnamLectureNotesVol2_20200210.pdf