Toric spaces being non-simply connected, it is possible to find in such spaces some loops which are not homotopic to a point: we call them toric loops. Some applications, such as the study of the relationship between the geometrical characteristics of a material and its physical properties, rely on three-dimensional discrete toric spaces and require detecting objects having a toric loop. In this work, we study objects embedded in discrete toric spaces, and propose a new definition of loops and equivalence of loops. Moreover, we introduce a characteristic of loops that we call wrapping vector: relying on this notion, we propose a linear time algorithm which detects whether an object has a toric loop or not. © 2008 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Chaussard, J., Bertrand, G., & Couprie, M. (2008). Characterizing and detecting toric loops in n-dimensional discrete toric spaces. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4992 LNCS, pp. 129–140). https://doi.org/10.1007/978-3-540-79126-3_13
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