Characterizing and Detecting Toric Loops in n-Dimensional Discrete Toric Spaces

  • John Chaussard
  • Gilles Bertrand
  • Michel Couprie
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4992)


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.


Base Point Fundamental Group Homotopy Class Null Vector Linear Time Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • John Chaussard
    • 1
  • Gilles Bertrand
    • 1
  • Michel Couprie
    • 1
  1. 1.LABINFO-IGM, CNRS UMR8049 ESIEEUniversité Paris-EstNoisy le Grand CEDEXFrance

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