Forma, Vol. 22 (No. 2), pp. 191-197, 2007

Betti Numbers of Defects Field

Kazuhito Yamasaki

Department of Earth and Planetary Sciences, Faculty of Science, Kobe University, Kobe 657-8501, Japan
E-mail address:

(Received April 10, 2006; Accepted Mach 10, 2007)

Keywords: Betti Numbers, Defects, Dislocations, Disclinations, Topology

Abstract. The algebraic topological aspect of defects field is considered by using the useful topological invariant: Betti numbers. We suggest that the topological nature of the dislocation field is expressed in terms of "strength" of the dislocation corresponding to the change in the first Betti number. We also show that Frank vectors of the disclinations are related to the first Betti number.

[Full text] (PDF 120 KB)