Cycle classes as topological invariants of crystal structures
- 1 September 1994
- journal article
- Published by Walter de Gruyter GmbH in Zeitschrift für Kristallographie - Crystalline Materials
- Vol. 209 (9) , 709-713
- https://doi.org/10.1524/zkri.1994.209.9.709
Abstract
Cycle class sequences are introduced as topological invariants of crystal structures. A cycle class is a class of translationally equivalent cycles, and a cycle class sequence is a sequence of numbers C 3, C 4,…, C n,…, where C n is the number of classes of cycles of length n. Such a sequence consists of integers and is the property of the whole crystal structure. In addition, another type of sequence, called cycle sequence, is defined. Cycle sequences are attributed to individual atoms and may be used to probe the topological equivalence or inequivalence of two atoms.Keywords
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